Yes, both sides oversimplify ... yet another reason that privationism / Chazalism present the best theological approach.
So ... a priest is giving a sermon from the pulpit and makes a heretical statement. Aunt Helen (Father Cekada's heroine) recognizes the heresy for what it is, valiantly stands up, and declares him to be outside the Church. Is he a manifest heretic now?
Priest says, just a mental lapse and slip of the tongue, where I forgot to say the word "not". Was he a manifest heretic? Certainly he uttered heresy, and ... it was in fact manifest ... but it was clearly lacking in pertinacity. So ... no.
Next week a different priest comes and utters a different heresy. Once again, Aunt Helen shows herself to be an intredpid defender of the faith and denounces the heresy. Having learned her lesson from the previous week, she asks the priest if he meant to say what he said. Priest says he did mean to say it. But then Aunt Helen pulls out her pocket copy of Denzinger, the edition before Rahner's, and shows him where the proposition was condemned as heresy. Priests apologizes and retracts the heretical statement. Was he ever outside the Church? No, since, again, pertinacity was lacking.
Yet another week goes by, and a third priest proclaims a heresy. Aunt Helen, armed with her Baltimore Catechism No. 1, having not yet graduated to No. 2 ... goes through the previous steps, but the priest sticks to his guns, telling Aunt Helen that she doesn't know what she's talking about. Is this priest no longer a member of the Church? Just because Aunt Helen says so? So, let's say Aunt Helen was wrong. OK, then, he never lost membership in the Church. But let's say Aunt Helen did happen to get it right, and the priest was wrong and what he said was in fact heretical? Well, the priest goes back to his bishop, and the bishop, renowned for his great knowledge of Catholic doctrine, tells the priest, "Well, sorry to tell you this, but Aunt Helen was right. That's rather embarrassing. I'll have to get the rector of the seminary on the line to find out what's going on over there." Priest then admits his error and changes his mind -- and the seminary rector is relieved of duty. Did he ever lose his membership in the Church? No ... even if the seminary rector lost his job. Why? Because his heresy was not formal, i.e. the only reason he held to it was because he did not think it was condemend by the Church or the opposite was taught as dogma by the Church ... his only crime was not taking Aunt Helen's word for it. But, then ... who really would, since she cries wolf on heresy against every few priests who come by.
So, as a result of these cases, the heresy that results in loss of membership in the Church must be 1) manifest, 2) pertinacious, and 3) formal (where it at least implicitly rejects the Church's teaching authority).
Then what if there are a bunch of Catholics who claim something is here, and another group that say the opposite is heresy, such as when the Thomists and Molinists were battling it out. Are either group heretical? No, since there's enough disagreement among presumably-well-meaning Catholics that it's hard to discern the truth of the matter.
I've long told the SVs that personal manifest heresy is absolutely the wrong approach to this crisis, and you can argue either way until you're blue in the face and never come to a conclusion that can satisfy everyone.
In addition, despite multiple challenges, both here on CI and to a larger audience on X, I have requested evidence for Montinin having been a manifest heretic before he took office, and outside of his actually beginning to teach the Church and approve (allegedly) heretical teaching. Crickets. No one has ever produced anything. You could find more about Roncalli than Montini, since Montini evidently cared more about manning soup kitches and building stuff (like most bishops just prior to Vatican II) than about abstract, abstruse, and "pie in the sky" subjects like theology. In fact, and this was a terrible fault of Pius XII, the vast majority of bishops were organizers, builders, and fundraisers, while knowing very little about Catholic theology, despite their chief duty (as explained during the Rite of Consecration) being to teach and defend the faith. That's why most of them had to bring so-called "periti" in tow with them to Vatican II, since they lacked competence, and, then, having vouched for their periti, went off to the "Bar Jonah" to pass the time while deliberations, driven by their Modernist periti, took place. For them, if their peritus seemed smart, articulate, and had a degree from one of the Roman institutions, that was good enough for them ... and for all they cared, really. Since most of them weren't even fluent in Latin (listen to +Cushing's attempt to offer Mass at the risk of developing grave scruples), after returning from Happy Hour at Bar Jonah, they might nudge their "peritus" ... "Hey, Rahner ... should I vote for this?" Rahner: "Absolutely, yes ... it will transform the Church."
In any case, there's zero evidence that's ever been presented to establish that Montini had been a manifest heretic prior to his teaching error at Vatican II. Big problem. If you think it suffices to determine a non-papacy due to manifest heresy ... only after he starts teaching heresy, that guts the entire Magisterium. That way, if I were an Old Catholic type, and disagreed with some dogmatic definition, I could simply declare the Pope to be really a non-Pope and reject the teaching. Problem solved. ... Bigger Problem created. You could never, then, have an a priori certainty regarding any dogma proclaimed by a Pope, since you could simple argue backwards from what you decided was false dogma to the illegitimacy of the one defining it. This guts the entire Magisterium. See, you were still considered Catholic prior if you denied papal infallibility prior to the dogmatic definition at Vatican I. But, once it was defined, you accepted the teaching with the certainty of faith, and retracted the previous error. That's how it should work. But with the principles of SVism, not necessary, since Aunt Helen can just depose the pope for you.
Nor has any SV ever produced a working viable solution to prevent Aunt Helen from starting to depose any pope from her armchair whose teaching she didn't care for, Pius XII, Pius XI, Pius IX, Leo XIII, and even St. Pius X. Father Cekada in his so-called "refutation" of my early "Pope-Sifting" essay (aka "article"), amid a flurry of personal attacks (rooted mostly in his ignorance of the fact that I had not in fact published any article nor was responsible for a good portion of its content), came up with one desperate idea that he slips in after four pages of not even coming up for air and catching his breath from the rattling off his stream of insults. He says that Dogmatic Facts (such as is the legitmacy of a Pope) is something that's "historical". So he declares, making an embarrassing blunder, that this means you cannot impugn the legitimacy of a past pope ... unless there was someone alive during his reign who had done so. Apart from the fact that this does not suffice, since it's quite possible many did exactly that to Pius IX after Vatican I, and there may even have been a bold ancestor of Aunt Helen alive during the reign of St. Pius X ... the embarrassing blunder comes from his misunderstanding of the term "historical", which does not mean "past" but simply refers to something that's in the nature of an event or a fact, rather than a proposition, so that a normal dogma involves the assent of faith to a proposition, a dogmatic fact refers to an event or a circuмstances, something historical IN NATURE, and not involving a "past" time. Apart from this single attempt, which nevertheless resulted in an epic fail, no SV has ever produced a principle that could restraing the indefatigable Aunt Helen in her crusade to find and denounce heresy wherever she saw it.
No, where it comes to something a serious as the legitimacy of a Pope, there must be some role for the Church to play, and it cannot be left up the musings of Aunt Helen, or even Father Cekada himself. That's again where Sedeprivationism comes in, and where I first coined, largely tongue-in-cheek, the term "Sededoubtism" (which Sean Johnson has actually adopted of late), where someone is not to be counted as a schismatic who refuses submission to a putative Pope based upon well-founded and relatively widespread (among orthodox believers) questions about his person or (the legitimacy of) his election. This would put a Pope into the "papa dubius" category, where the accompanying maxim indicatest that "papa dubius nullus pappa" (for all practical intents and purposes) and therefore into what Father Chazal aptly describes as a "state of suspension", until resolved definitively one way or another by the Church.
Let's take the Great Western Schism. If I believed that Pope A was the true pope, if Pope B had proclaimed a dogma during the Schism, would I have been a (formal) heretic for rejecting the dogma? No, since there wasn't an antecedent, or a priori, certainty of faith regarding the legitimacy of Pope B, and I wasn't alone in questioning him. EVENTUALLY, the Church intervened and decided who had been the legitimate Pope. At that point, had the legitimate Pope, let's say it was Pope A, been the true Pope, any dogma that he defined would have been accepted by the Church in hidsight as being a true dogma to be believed under the pain of heresy and separation from the Church. At some point the Church, not Aunt Helen, despite her zeal, energy, and theological acuмent ... must be The Final Decider, and if that means that the Pope is more in a "dubius" situation (contrary Bishop Sanborn's mistaken condemnation of "Opinionism") than anything else, in a state of suspension, perhaps a material but nor formal pope ... or something along those lines, rather than definitively a non-Pope. Archbishop Lefebvre often hinted that he expected a Future Pope or Council to declare these men Anti-Popes once and for all, and I too share that Opinion.
So the argument from personal manifest heresy is largely unworkable, since short of Prevost coming out an saying, "I don't believe Christ actually rose from the dead." or "There are Four Divine Persons in the Holy Trinity" ... it's just too difficult a case to make.
Onto the other angle, then, namely, from the heresies and errors TAUGHT by these putative Popes and from their having promulgated a form of Public Worship that offends God and harms souls, and then canonizine a veritable rogue's gallery of non-saints, an argument made modo tollentis.
So, where this breaks down is the SVs, in reaction against R&R who reduce the protection over the Church by the Holy Ghost to the 1-or-2-per-century solemn dogmatic definitions, leaving 99.9% of the Magisterium up for grabs and fair game, including allowing for nearly all of it to be polluted and corrutped, so long as those solemn definitions are protected. SVs then inanely join battle on this front, but absurdly extending the scope of infallibilty to include nearly every time a pope passes wind, even if it isn't through his lips, some even to any book that has received an imprimatur, leading to a dispute that can never be resolved. "That should have been infalible." "No it shouldn't have." "Yes it should." "No it shouldn't." "I know you are, but what am I?" ... this is pretty much the deplorable state we're in regarding this debate. While many SVs exalt the authority of pre-Vatican II theologians as if they were themselves a rule of faith, in a position that I have coined "Cekadism" (something, BTW, which the reputable and orthodox Msgr. Fenton, a true theologian, actually rejected as absurd), so while they puff up the authority of theologians, they are unable to cite a SINGLE THEOLOGIAN prior to Vatican II that had ever extended papal infallibility to the extent that SVs do. On this topic, I recommend the remarkably well-balanced discussion on the matter by Msgr. Fenton in his essay on the Authority of Papal Encyclicals, which, despite the name, does an admirable job of discussing the matter.
Now, this is where SVs missed the boat. Msgr. Fenton also describes a different type of infallibility enjoyed by the Church overall and the Papal Magisterium in particular, that of infallible safety, where a body of teaching could not be radically in error, and where said errors can result in fatal damage to faith and morals, where Catholics who follow that teaching risk losing their souls as a result of having done so. This speaks more to the infectibility of the Church rather than to "infallibility in the strict sense" (an apt term coined by Msgr. Fenton). Here's the basic argument from that. While you could go back and forth on whether this, that, or another teaching meets the notes of infallibility defined by Vatican I, you've clearly crossed a line into indefectibility where Catholics not only may, but even must, break from submission to the hierarchy in their Universal Teaching and Discipline, in order to please God and to save their souls. If things can get so bad where Catholics wouldn't even be able to consider themselves as practicing the Catholic Religion if they remained in the Conciliar Church, where they endanger their souls and risk offending God and embracing grave error (if not heresy) against the Catholic Faith, you've crossed the line into a defection of the Church in her mission, since that is in fact THE primary mission of the Church, to defend faith and morals, and to facilitate the salvation of souls. That cannot happen.
So SVs have missed the forest of indefectibility in getting distracted by the trees of infallibility, and as a result feel the need to exaggerate the scope of infallibility to absurd lengths that no Catholic theologian has ever held.