It shall appear to WHOM? To Grandma Jones? I knew a guy who considered Pius IX a non-pope because it "appeared" to HIM that Pius IX had embraced heresy.
That's between him and God. But there is such a thing as manifest heresy which clearly and explicitly contrary de fide teachings. Why is the ability to know this constantly questioned in general because many people don't possess the necessary faculties to discern it?
If my priest stands before the congregation and says:" I've converted to Islam", is his apostasy, in good conscience, not to be taken as an objective fact? If a bishop states publically that Jesus Christ did not come in the flesh and die on the cross, is there some reaosonable doubt left somewhere as to my obligation to shun him as a heretic? And if an apparent pope teaches moral relativism and gradualism as part of his authentic magisterium and, after being corrected, persists in this, what am I to think?
I do not know with certaintiy, but my doubt would be sufficient that in good conscience I cannot accept him, but neither will I publically denounce him: rather I will shun and let God judge my intentions, as he has not given me sufficient knowledge to make a final judgment.
And I am apparently permitted to act according to my conscience in discernment of this:
7. Finally, [by this Our Constitution, which is to remain valid in perpetuity, We] also [enact, determine, define and decree]:- that any and all persons who would have been subject to those thus promoted or elevated if they had not previously deviated from the Faith, become heretics, incurred schism or provoked or committed any or all of these, be they members of anysoever of the following categories:
(i) the clergy, secular and religious;
shall be permitted at any time to withdraw with impunity from obedience and devotion to those thus promoted or elevated and to avoid them as warlocks, heathens, publicans, and heresiarchs (the same subject persons, nevertheless, remaining bound by the duty of fidelity and obedience to any future Bishops, Archbishops, Patriarchs, Primates, Cardinals and Roman Pontiff canonically entering).” - Cum ex
Withdraw and avoid.
If there's division in the hierarchy, which an "imperfect council" implies, it all boils down to having to make an act of personal discernment until such time as a new pope is elected (and even then ...). Such a council may help many, but it is not a solution.
But that's precisely why I have been sede-agnostic ... totally confused ... what I am NOT going to do is become a formal schsimatic who akcnowledges a pope but refuses to submit to him.