Further Thoughts on the Validity of Post-Conciliar Papal Claimants
The Catholic faith provides us with the necessary principles, and together with our God-given intellect, equips us to judge matters prudently in view of our salvation.
Readers often write to me asking what my exact position is on a particular aspect of the faith. My answer is straightforward: I hold the Catholic position. The same question inevitably arises in relation to the papacy, and again my response is the same—I adhere to what Catholicism itself teaches. The Catholic faith provides us with the necessary principles, and together with our God-given intellect, equips us to judge matters prudently in view of our salvation.
For this reason, I am not going to frame things in terms of “my position,” as I have often found that such labels tend to obscure rather than clarify. Instead, as I did in my recent articles The Question About the Crisis We All Eventually Have to Face and Is This the Sanest Position for Faithful Catholics to Hold Regarding Post-Conciliar Popes?, I aim to present some of the Catholic teachings and arguments that have informed my conclusions. My hope is that this will assist in bringing greater clarity to the question of the validity of the problematic papal claimants of the past sixty-odd years.
Be aware that what follows is a lengthy essay, but I trust it will offer a few more pieces to this important and complex puzzle. As you read, I encourage you to keep a sheet of paper nearby and honestly assess figures such as Bergoglio and Prevost, considering whether, according to the demands of the Catholic faith, they can be regarded as true popes.
Who May Become Pope, How the Office Is Lost, and What Heresy, Apostasy and Schism Is
In Catholic canon law, the question of who may validly become Pope, and under what circumstances that office may be lost, has been carefully defined through centuries of legal, theological, and historical development. At its core, the Church maintains that a valid papal candidate must be a baptized Catholic male who possesses the use of reason and remains in full communion with the Church. These requirements, rooted in both tradition and codified law, establish clear boundaries excluding certain categories of individuals from eligibility. Women, children, those lacking sufficient mental capacity, the unbaptized, and anyone who is formally separated from the Church through heresy (o-oh! - ed), apostasy (double o-oh!- ed), or schism (probably already not looking good on that sheet!- ed) are all considered incapable of validly assuming the papal office.
To fully understand these exclusions, it is essential to clarify what the Church means by heresy and how it distinguishes between its various forms. In Catholic theology and canon law, heresy is defined as the obstinate denial or doubt, after baptism, of a truth that must be believed with divine and Catholic faith (like say, the doctrine that Jesus Christ is the Only Way by which we can be saved?! – ed). This definition contains several key elements: the individual must be baptized, the doctrine in question must be one definitively taught by the Church, and the rejection must be both knowing and persistent. Heresy, therefore, is not simply error, but a deliberate and sustained rejection of revealed truth.
The Church distinguishes carefully between material and formal heresy in order to account for differences in knowledge and intention. Material heresy occurs when a person holds an objectively incorrect belief about a matter of faith but does so without full awareness or deliberate intent to contradict Church teaching (A learned Pope can therefor hardly get off the hook on a claim of ignorance! - ed). Such error may arise from ignorance, misunderstanding, or inadequate formation. Because the individual does not knowingly reject the truth, material heresy does not incur canonical penalties and does not sever one from the Church.
Formal heresy, by contrast, involves a conscious and deliberate rejection of a defined truth of the faith, accompanied by obstinacy—that is, persistence in error even after the truth has been sufficiently explained. It is this willful resistance to authoritative teaching that transforms error into a grave offense against ecclesial unity. Under canon law, formal heresy incurs automatic excommunication (Oops, really?! - ed), meaning that the individual is considered to have removed himself from full communion with the Church. As a result, such a person is no longer eligible to hold ecclesiastical office, including the papacy.
Another important distinction concerns whether heresy is private or public. A person may hold erroneous beliefs internally without expressing them outwardly or may openly profess them in a way that becomes known to others (“Openly”? As in professing them in front of nearly 1.8 billion Catholics? - ed). Canonical consequences are primarily attached to public and manifest heresy, particularly when it causes scandal or confusion among the faithful. Private error, even when culpable, does not have the same juridical effects unless it becomes externally evident and obstinately maintained.
Closely related to heresy are the concepts of apostasy and schism, both of which also rupture communion with the Church. Apostasy refers to the total repudiation of the Christian faith, while schism involves the refusal to submit to the authority of the Roman Pontiff or to remain in communion with the members of the Church subject to him. Like formal heresy, both offenses incur automatic excommunication and result in exclusion from ecclesiastical office. These distinctions underscore the Church’s insistence that anyone who holds authority within it must remain fully united in faith and governance.
The process by which a Pope acquires authority is equally precise. According to both the 1917 and 1983 Codes of Canon Law, a legitimately elected candidate gains full and supreme jurisdiction immediately upon freely accepting the election. If the individual is not already a bishop, he must be ordained without delay. This moment of acceptance is decisive, it is not merely the election itself, but the free and conscious acceptance of that election that confers papal authority.
The Church has also consistently emphasized that the election must be entirely free. Any form of coercion, bribery, or simony renders the election invalid by law. These prohibitions reflect a longstanding concern for preserving the spiritual integrity of the papacy and ensuring that the office is conferred solely through legitimate and uncorrupted means. Modern norms governing papal elections continue to reinforce these principles by strictly forbidding external interference or manipulation.
While the criteria for papal eligibility are clearly defined, the question of how a Pope may lose office is more complex. Canon law recognizes only a limited number of ways in which the papacy can become vacant. The most obvious is death. Another is voluntary resignation, which must be made freely and properly manifested. Importantly, no acceptance by any other authority is required for a papal resignation to be valid. Historical examples, including the resignations of Celestine V, Gregory XII, and Benedict XVI, demonstrate that this provision has been applied in practice and remains a legitimate means by which a pontificate may end.
In contrast, the idea of forcibly removing a Pope is firmly rejected by Catholic doctrine. The First Vatican Council affirmed that the Roman Pontiff is judged by no one, establishing that no earthly authority has the power to depose a valid Pope. This principle has been consistently upheld in canon law, which explicitly excludes any form of appeal or recourse against papal decisions. The Pope, once validly elected and having accepted office, holds supreme authority in the Church and cannot be subjected to external judgment. But we will return to this.
A more debated and complex question concerns the possibility of a Pope falling into formal heresy after his election. Some theologians argue that, because formal heresy separates a person from the Church, a Pope who becomes a heretic would automatically lose his office. Others contend that, since no authority exists to judge or declare the Pope deposed, there is no clear juridical mechanism to effect such a loss. While the principles regarding heresy are well defined, their application to the papacy remains a matter of ongoing debate rather than settled doctrine.
Historical cases provide insight into how these principles have been interpreted over time. Instances such as the deposition of Pope Silverius by secular authorities or the posthumous condemnation of Pope Formosus illustrate attempts to interfere with the papacy that were later judged illegitimate. During the Western Schism, the Council of Constance addressed competing papal claimants by accepting the resignation of Gregory XII and deposing antipopes. However, these actions did not establish a general precedent for deposing a universally recognized Pope, but rather resolved an extraordinary crisis involving disputed legitimacy.
Over time, both the 1917 and 1983 Codes of Canon Law have reaffirmed the same essential principles regarding papal eligibility and authority. While certain procedural norms have developed, the fundamental requirements—that the Pope be a baptized Catholic male in full communion with the Church, freely elected, and properly accepting the office—have remained unchanged. Likewise, the principle that no human authority can depose a valid Pope continues to be a cornerstone of Catholic ecclesiology.
Can a Pope Remain Truly Pope While Persistently Teaching Error?
A particularly complex and much-debated question in Catholic theology concerns whether a Pope can remain a true and legitimate pontiff if he were to persistently teach doctrines contrary to the Catholic faith. This issue lies at the intersection of ecclesiology, canon law, and the theology of heresy, and it has never been definitively resolved by an infallible teaching of the Church. As a result, theologians have proposed different explanations, each attempting to reconcile the Church’s teaching on papal authority with the possibility of doctrinal error.
At the outset, it is important to distinguish between different types of papal teaching. The doctrine of papal infallibility, defined by the First Vatican Council, holds that the Pope is preserved from error only when he definitively proclaims a doctrine of faith or morals to be held by the whole Church. Outside of these specific conditions, a Pope may express theological opinions, disciplinary decisions, or pastoral teachings that are not guaranteed to be free from error. Therefore, the mere presence of mistaken or even problematic statements does not, in itself, call into question the validity of a Pope’s office.
The more serious question arises when one considers the possibility of a Pope who persistently and knowingly teaches what is contrary to the faith. In such a case, the issue is no longer one of isolated error but of potential formal heresy. As previously noted, formal heresy involves the obstinate and deliberate rejection of revealed truth and results in automatic excommunication, which separates a person from the communion of the Church. Since communion with the Church is a necessary condition for holding ecclesiastical office, this raises the theoretical possibility that a heretical Pope could lose his office.
Some theologians, particularly in the classical tradition, have argued that a Pope who becomes a manifest and obstinate heretic would cease to be Pope ipso facto, that is, by the very fact of his heresy. According to this view, the loss of office would not require a formal deposition by any authority, since the individual would already have separated himself from the Church. In this understanding, the Church would not be judging the Pope, but rather recognizing a fact that has already occurred.
May the Laity Doubt the Validity of a Pope?
Another important and sensitive question concerns whether members of the laity may legitimately doubt the validity of a reigning Pope. This issue touches on the nature of ecclesial authority, the visibility of the Church, and the limits of private judgment within Catholic life. While the Church calls the faithful to unity and obedience toward the Roman Pontiff, theologians have long recognized that extraordinary circumstances can raise questions about legitimacy, particularly in times of crisis or uncertainty. And to call the post-Vatican II situation a crisis, is a euphemism that underemphasizes the severity of the current rampant and all-encompassing heresy and apostasy.
Under normal conditions, the Church presumes the validity of a papal election once it has been peacefully accepted by the Church as a whole. This principle, sometimes referred to as “universal peaceful acceptance”, has been widely regarded by theologians as a strong sign, and even a guarantee, of legitimacy. When the bishops and faithful throughout the world recognize a man as Pope, this consensus is taken as evidence that the election was valid and that he truly holds the office. In such cases, the laity are not only discouraged but generally considered unjustified in privately disputing the Pope’s legitimacy.
However, Catholic theological tradition also acknowledges that this presumption is not purely blind or irrational. In situations where serious and objective doubts arise (and boy, are they! -ed), some theologians have argued that the faithful may withhold assent until the matter is clarified. This position does not imply a right to casual or subjective dissent, but rather a cautious recognition that legitimacy depends on objective conditions established by divine and ecclesiastical law.
In this context, the teaching of St. Robert Bellarmine is often cited. Bellarmine, a Doctor of the Church, addressed questions surrounding papal authority and heresy in considerable depth. While he strongly defended the primacy and authority of the Pope, he also acknowledged that a manifestly heretical individual could not be a true member of the Church and therefore could not be its head. By extension, if a man were widely believed to be Pope but was in fact incapable of holding the office due to such a defect, Bellarmine’s reasoning implies that the faithful would not be bound to accept him as a true pontiff.
At the same time, Bellarmine and other classical theologians emphasized that the determination of such matters is not entrusted to private individuals acting on personal judgment alone. The Church is a visible and hierarchical society, and questions of such magnitude ordinarily require recognition by the Church as a whole, particularly by the bishops. But, if almost the whole visible “church” finds itself in a state of apostasy, as is the case now, then this becomes problematic as you can no longer rely on the judgement of its hierarchy. The question then arises, is the “church” currently claiming to be the Catholic Church actually the Catholic Church? I would argue no, because it teaches a whole body of doctrine that clearly contradicts Catholicism.
Under ordinary circumstances, the faithful are bound to accept the legitimacy of the Roman Pontiff as recognized by the Church. Nevertheless, in rare and exceptional situations where serious and objective doubts arise, such as has been the case the past 60 years, theologians such as St. Bellarmine suggest that the faithful may experience and even express doubt.
But What About the Vatican I Teaching That the First See is Judged by No One?
We have to fully accept the teaching of the First Vatican Council that the first see is judged by no one (prima sedes a nemine iudicatur). This is a dogmatic truth of the Catholic faith. However, the crucial point is this: that principle applies only to a true and valid pope. It does not, and cannot, apply to someone who is not in fact pope.
The argument often assumes what must first be proven: that the man in question actually possesses the papal office. But if a man publicly defects from the Catholic faith through manifest heresy, then he ceases to be a member of the Church. And since the pope must be a member of the Church, such a man cannot be pope. Therefore, in concluding that a manifest heretic is not pope, we are not “judging the pope” at all—we are recognizing that the papal office is not occupied.
This distinction is essential. There is a fundamental difference between judging a pope (which no one may do) and recognizing that a claimant to the papacy lacks the necessary condition—membership in the Church—to hold that office. The Church does not lose her visibility or coherence by this recognition, but rather preserves her indefectibility, since it would be impossible for the true Church to be headed by someone who professes error against the faith.
This position is not novel. It is grounded in the theological tradition represented by figures such as St. Bellarmine and Francisco Suárez, who considered the hypothetical case of a heretical pope. As I have already pointed out, Bellarmine, in particular, argued that a manifest heretic would automatically cease to be pope, not by any human judgment or deposition, but by the very fact of his heresy. In such a case, the Church does not act upon the pope; rather, it acknowledges a reality that has already occurred.
Moreover, the teaching of Vatican I itself must be properly understood. The council defined the conditions under which the pope teaches infallibly—namely, when he speaks ex cathedra. It did not teach that every statement or action of a pope is free from error, nor did it address in detail the question of a pope who falls into heresy outside of those infallible acts. Therefore, appealing to Vatican I does not resolve the issue unless one first establishes that the individual in question is truly pope and has not defected from the faith.
Finally, the principle of the Church’s indefectibility must be upheld. The Church cannot officially teach error, nor can she be led into heresy by her visible head. If, therefore, one concludes that certain recent claimants to the papacy—particularly in the aftermath of the Second Vatican Council—have promulgated teachings contrary to the prior magisterium, then the only way to preserve the indefectibility of the Church is to conclude that such men were not true popes.
I do not deny that the first see is judged by no one. Rather, I insist that this principle cannot be used to shield from scrutiny someone who lacks the very authority it presupposes. Recognizing that a manifest heretic is not pope is not an act of judgment over the papacy—it is a defense of the papacy itself.
What is the difference between someone formally and materially occupying the seat of Peter?
In order to understand the present crisis in the Church, it is also helpful to distinguish between two ways in which a man may be said to occupy the See of Peter: materially and formally. This distinction, rooted in classical Catholic philosophy, helps clarify how someone may appear to be pope externally while not truly possessing the authority of the papacy.
To occupy the papal office materially means that a man has been elected according to the outward procedures of the Church and is publicly recognized as pope. He resides in Rome, governs the visible structures of the Vatican, and is accepted by the world as the successor of St. Peter. In this sense, he possesses the external aspect of the papacy. From all appearances, he is pope.
However, to occupy the papal office formally is something deeper. It means that the man truly holds the authority of the papacy and that he has received jurisdiction from Christ and is a genuine successor of St. Peter in the full theological sense. This requires not only a valid election, but also that he be a member of the Catholic Church, adhere to the true faith, and intend to fulfill the office as instituted by Christ.
The distinction becomes necessary when one considers the possibility that a man might fulfill the external conditions for being pope while lacking the internal disposition required to actually possess the office. If a man were to publicly adhere to doctrines contrary to the Catholic faith, he would thereby place himself outside the Church. Since the pope must be a member of the Church, such a man could not truly hold the papal office, regardless of his external status.
In such a case, it can be said that the man occupies the See of Peter materially but not formally. He holds the position in an outward and visible sense, but lacks the authority that gives the office its true reality. The structure remains, but the essential principle is absent.
This distinction helps preserve two essential truths at once. On the one hand, the Church must remain a visible society with recognizable structures, including the papacy. On the other hand, the Church cannot be headed by someone who does not profess the Catholic faith. By distinguishing between material and formal occupation, one can acknowledge the external reality of a papal claimant while maintaining that the authority of the papacy itself is not truly present in him.
An analogy may help illustrate the point. One might think of a body without a soul: it retains the outward form of a living thing, but lacks the principle that gives it life. In a similar way, a materially occupied papal office without formal authority retains its visible structure, but not its true nature.
Thus, the difference can be summarized simply: a man who occupies the See of Peter materially has the appearance and external position of the papacy, while a man who occupies it formally truly possesses the authority and office established by Christ.
But Shouldn’t We Measure the Pope Only by His Ex Cathedra Pronouncements?
Again, there is no reason to not accept the teaching of the First Vatican Council that the pope is infallible only when he speaks ex cathedra. This is a defined dogma of the Catholic faith. However, the common argument that follows, namely, that we should judge the orthodoxy of a pope solely on his ex cathedra statements, is a serious distortion of what the Church teaches about the papacy and her magisterium.
The definition of papal infallibility at Vatican I was never intended to imply that everything outside of ex cathedra pronouncements is theologically unreliable, inconsequential, or even potentially heretical without consequence. On the contrary, the Church also teaches that the ordinary and universal magisterium is protected from error. The pope, even when not speaking ex cathedra, is still the visible head of the Church and the guardian of the deposit of faith. His ordinary teaching cannot contradict what the Church has always taught.
If, therefore, a man who claims to be pope were to publicly and persistently teach doctrines that contradict the prior magisterium, the problem cannot be dismissed by saying, “he has not spoken ex cathedra.” A true pope cannot be a habitual source of doctrinal confusion or error for the faithful. To suggest otherwise is to reduce the papacy to a rare and almost abstract function—an occasional voice of infallibility surrounded by a sea of fallibility and potential error.
Such a view empties the papal office of its practical purpose. The pope is not merely an infallible teacher on rare ceremonial occasions; he is the perpetual principle of unity and orthodoxy in the Church. If the faithful must constantly sift, reinterpret, or even resist his ordinary teachings in order to remain Catholic, then the papacy ceases to function as a reliable guide and instead becomes a potential danger to souls. This is incompatible with the very reason Christ instituted the papacy.
Furthermore, the indefectibility of the Church must be preserved. The Church cannot lead the faithful into error in matters of faith and morals, whether through extraordinary or ordinary teaching. If a supposed pope were able to promulgate doctrines or practices harmful to the faith on a regular basis, while remaining a true pope simply because he avoids ex cathedra definitions, then the Church would no longer be a trustworthy guide to salvation.
The theological tradition also supports this conclusion. As articulated by figures such as St. Bellarmine, a man who becomes a manifest heretic ceases to be a member of the Church and therefore cannot hold ecclesiastical office, including the papacy. This principle does not depend on whether the heresy is taught ex cathedra. What matters is the public adherence to error itself, which is incompatible with membership in the Church.
In reality, the appeal to “only ex cathedra pronouncements” serves to lower the standard of what is expected from the papacy in order to accommodate apparent doctrinal deviations. But this comes at too high a cost. It forces one to accept that the visible head of the Church may regularly mislead the faithful, so long as he refrains from invoking a specific formula of infallibility. Such a position undermines both the authority and the purpose of the papacy.
A more coherent conclusion follows: if a man’s public teaching consistently conflicts with the perennial doctrine of the Church, the issue is not that he is a true pope exercising a non-infallible and therefore unreliable magisterium. Rather, it is that he does not truly possess the papal office at all.
Thus, we do not deny the limits of ex cathedra infallibility. We deny that those limits can be used to justify accepting as pope someone whose ordinary teaching appears to contradict the Catholic faith.
Now Let Us Take a Closer Look at Leo XIV and Then You Decide!
A major theme that has emerged thus far in Leo XIV’s papacy, as with his predecessor, is the promotion of ecumenism and religious pluralism. Statements encouraging unity among different Christian denominations, and even across religions, shows that for Robert Prevost doctrinal differences are of little importance. This shows a consistent denial of the belief that the Catholic Church alone possesses the fullness of truth and is therefore the promotion of religious indifferentism.
Another hallmark of his papacy is his doctrinal relativism. Expressions implying that the Church does not uniquely “possess the Truth,” or that theological disagreements should be set aside, are undermining the idea of objective, revealed truth. This approach reduces doctrine to something negotiable or subjective, rather than fixed and authoritative. Again, totally in contrast to Catholic teaching.
Leo XIV’s teachings on salvation is also heterodox to say the least. He often uses language that broadens the possibility of salvation outside the visible Church, or that emphasizes salvation “for all,” which is a clear leaning toward universalism which was condemned by the Church.
Questions of moral theology raises more red flags. His statements cautioning against “rigidity” or emphasizing pastoral sensitivity are downplaying sin and moral absolutes and seriously jeopardizing souls. In particular, his ambiguity on issues such as divorce, remarriage, or same-sex relationships are evidence of moral relativism.
It is also clear that his theology contains an imbalance between God’s mercy and justice. His strong emphasis on mercy alone, combined with the rejection of images of a “vengeful God,” is neglecting divine justice, punishment, and the reality of hell, and presents a one-sided understanding of God’s nature.
Prevost further emphasizes topics such as climate change, migration, and global cooperation, and in doing so, shifts attention away from the Church’s spiritual mission toward worldly concerns. This shift is a form of naturalism, where temporal priorities overshadow eternal ones.
There are also Concerns about his ecclesiology. The moment he took office he started describing the Church as “synodal,” dialogical, and evolving. It has become clear that his mission is redefining it from a divinely established institution into a human-centred community.
Furtermore, his openness to expanded leadership roles for women and ambiguity toward movements advocating women’s ordination, is conflicting with the traditional teaching of an all-male priesthood.
Interreligious relations, especially with Judaism, are another point of contention. A strong emphasis on dialogue and mutual respect, without explicit calls for conversion, is again minimizing the necessity of Christ for salvation. This lack of a call for conversion has become an ever-growing vacuum in the Synodal Church, and one of its main characteristics.
Certain of his statements have been potentially blasphemous and doctrinally problematic. These include interpretations of miracles as symbolic rather than literal, and comments suggesting that Bergoglio is in heaven.
Prevost is also an ardent advocate of the evolution of doctrine, adaptation to contemporary culture, and personal experience in theology. All of these are tell-tale signs of modernism, which, again, has been condemned by the Church.
Allegations of participation in non-Christian or symbolic rituals, such as the 1995 Pachamama incident, has recently surfaced, and indicates that the man now claiming to be pope, participated in idolatry and pagan worship. He has also been involved in other events incorporating indigenous or environmental symbolism which are acts of syncretism and idolatry.
Finally, his emphasis on unity over doctrinal division is again pointing to an agenda that has nothing to do with the protection of the deposit of faith. His statements suggesting that opposition or conflict between groups should be avoided are placing false harmony above truth. This undermines the idea that adherence to truth may, at times, necessarily lead to division.
I have only broadly touched on some categories of infringement here, and not even delved into the long list of specific atrocities he has committed in less than a year in office. There is no space or time here. With the technology at hand and with access to excellent websites such as Novus Ordo Watch and WM Review you have no excuse not to make a thorough investigation into the matter.
To conclude. As I have said before, I do not want to dictate to my readers what position they must assume. I would rather provide you with the tools to come to your own conclusion.
That being said, I want to remind you that each one of us have the duty and obligation to work out our salvation with fear and trembling.
May God have mercy on us…
Our Lady, Co-redemptrix, pray for us…
Our Lady, Mediatrix of all Graces, pray for us…
Viva Christo Rey!
Also Read:
Leo XIV Wants to “Generously” Include TLM Catholics but Only Within Vatican II Guidelines
Latest Proposal for TLM is Offensive, Arrogant, and Misses the Point Entirely



Man, this is so confusing. To me, there may be a pope somewhere but he is clearly not in the Vatican and he is not visible. If he exists, he may not even know he is pope. Or, there may not be a pope at all currently. Regardless, to me, any validly ordained and consecrated bishop - that is, one who is not a heretic or has not been ordained or consecrated by a heretic - has all the powers he needs to supply the means of grace and to govern his flock as defined by his consecration.
The main things I look for are valid ordination/consecration, and orthodoxy as defined by the Council of Trent.
Currently, I am a layman in the SSPX (I am not thrilled by its use of the 1962 missal but can live with it). Now, if the episcopal consecrations this July, produce an excommunication of the SSPX by the Synodal church, I expect to become a sedevacantist. If after being excommunicated by the post-conciliar church, the SSPX continues to try to cater to or reconcile with the synodalists in Rome, I’ll be forced to leave the SSPX.
Don’t get me wrong here… I want and need a pope. But we are living in desperate times of mass apostasy and every layperson is going to have examine themselves and take a stand before God. Work out your salvation in fear and trembling, indeed!
If I am reduced to praying my rosary at home and reading the Douay-Rhiems Bible and the DeHarb’s catechism, so be it. This is the price of hundreds of years of modernist/renaissance-enlightenment thinking and lukewarm religion.
A few points that need clarification:
1) Heresy--Heresy is the rejection of any article of Divine and Catholic Faith, which theologians and Canonists say means that which has either been Divinely revealed or defined by the Church. Heresy, according to Pope Piau XII in Mystici Corporis, ipso facto (by the very fact) separates one from the Church. The distinction between "formal" and "material" is for canonical, or legal, purposes. Public heresy, when it is accompanied by correction or admonishment that goes unheeded, is, according to theologians, sufficient to render one outside the Church. This is especially true for clerics, whose theological formation is much greater than laymen. They should know better: their correction is in their theological formation (one could argue that if they did not receive a fully Catholic formation, then they aren't Catholic anyway, and thus are not part of the Church, de facto). For this reason, the 1917 CIC held that a cleric who taught something that was either a) heretical, or b) could be interpreted as heretical, had 6 months to clarify or correct their statements, or would be considered formal heretics, under the law.
2) Loss of office due to heresy--Pope Celestine II declared that Nestorius, FROM THE MOMENT HE UTTERED HIS HERESY FROM THE PULPIT, had tacitly resigned his office as bishop. There were questions concerning the excommunications and usurpations that Nestorius had done while bishop of Constantinople. Celestine ruled that he was a heretic from the moment he publicly uttered his heresy.
3) Papal Infallibility--Pope Pius XI, in Quas Primas, teaches that the Church is "perennially preserved from teaching any error whatsoever". This would mean that when a valid Pope teaches something as Pope, we know that he is, at the least, not wrong. It may not be 100% precise, and there may be some things that need ironed out, but he's not wrong. Theologians hold that "Infallibility" as it is commonly used, refers to a teaching that is 1) "of the Faith", 2) necessary for salvation, 3) irreformable, and 4) revealed by God to the Apostles. As such, it is limited to four situations: 1) ex cathedra statements of popes on matters of faith and morals, 2) solemn definitions of Ecumenical Councils, 3) acts of the Universal, Ordinary Magisterium, and 4) the unanimous consent of doctors and theologians.
4) A Pope as heretic--It is true that the topic was not settled at the time of St. Robert Bellarmine, but by the Vatican Council of 1870, a general consensus had been reached: a Pope, when he public taught heresy, ipso facto lost his office. St. Alphonsus Liguori taught this, and this was reiterated by the Council Fathers when the topic of Papal Infallibility was discussed. At the Council, as recounted by the Cincinnati Archbishop Purcell (who was present at The Vatican Council), the question of a Pope who fell into heresy was raised, and the Council said that a) the mere THOUGHT that such a thing could happen was offensive to the office of the pope, and b) if it WERE to happen, the Pope would, by the fact of his heresy, lose his office without any declaration necessary, and the Church would then need to proceed to elect a new Sovereign Pontiff. This thought is present on the 1917 CIC, specifically Canon 188.4.
5) Invalid election and "universal peaceful acceptance"--The eminent theologian John of St. Thomas presents the case that the universal, peaceful (without coercion) acceptance of a claimant as Pope corrected any procedural or juridical complications in the election. In essence, that the whole Church accepted a claimant as Pope was evidence that he was, in fact, Pope. The issue is that "acceptance" includes treating the Pope as the Proximate Rule of Faith, and the Supreme Legislator, not just calling someone Pope and saying his name in the Te Igitur. However, "universal peaceful acceptance" does not mean a non-Catholic can be elected. This is outlined in Pope Paul IV's Cum Ex Apostolatus Officio, where he says, definitively, that public heretics cannot be validly elected to the papacy, even if 100% of the Cardinals accept him as pope, and he accepts it. If a claimant engaged in public heresy or apostasy prior to his election, and never publicly recanted, then he is not eligible to be elected Pope, because he is not Catholic.