Heretics are not Catholics. Catholics are baptized, confess the faith undefiled, and are subject to the (to any) reigning pope. Heretics do not confess the faith undefiled and hence are not Catholics.

The robber council of the 1960ies was a most solemn declaration of heresy of virtually all bishops of the time including the pope. E.g., to hold that there is a natural right to religious liberty, is heresy. All Fathers of that robber council are heretics having declared their heresies in a most manifest way. Their offspring is of the same kind.

Heretics are defectors, which — following Canon Law, Can. 188 §4 — lose their offices ipso facto (sentenced by the fact itself), or in other words latae sententiae (sentence automatically imposed, no further explicit sentence necessary).

But we do not even need Can. 188 §4. Communicatio in sacris with heretics is a sacrilege. It does not only not please the Lord. Communicatio in sacris includes participation in their rites as well as their teachings. A pope or a bishop cannot be someone we should shun, whose rites and teachings we must avoid.

Best post in this whole thread.
There is no consensus, even among the HANDFUL of theologians over the centuries who decided to even tackle this question to any degree.
So how can sedevacantists, or R&R, condemn their opponents as non-Catholic, unworthy to be Traditional Catholic, ban-worthy from CathInfo, etc.?

I completely believe in the R&R position. But I firmly hold that no one, not R&R and certainly not Sedevacantists, has a leg to stand on when they try to BIND THE CONSCIENCE OF OTHERS, or unilaterally excommunicate others, in this matter. Especially laymen excommunicating countless Catholics from their armchair.

Now an organization having a unity of doctrine, purpose, position is another matter. You can't have an organization tolerate widely differing (and contradictory) positions on the Crisis. There has to be unity within an organization.

As for variety of opinion or different paths, that's what the different Trad groups ("lifeboats") are for. But you can't have such variety within a single organization. "A house divided against itself cannot stand." That is why Archbishop Lefebvre expelled sedevacantists from his SSPX, etc. But he never said they were non-Catholic. Wrong, imprudent, etc. perhaps -- but he never claimed they were heretics. There's an important distinction to be noted there.

I agree with this as well.

Looking back at all the theologians who studied the matter of a bad pope, there are two main questions to discuss:
1.  Can the pope ever become a heretic and lose the faith?
2.  What happens if the pope becomes a heretic and loses the faith?

Most theologians never moved past question 1 because most could never conceive that the pope could even lose his faith.  So, as we are presently dealing with the situation of #2, the number of theological opinions on "what happens now?" is quite small.  There's definitely not a consensus on what happens even among the small # of theologians who attempted to answer the question.

I don't know why you believe most never got past #1.  Everyone admitted that a pope could fall into heresy until the 16th Century, when Albert Pighius first proposed the novel theory that a pope could not do so.  Pighius' novelty remained a minority opinion until the 20th Century.  It is true that Bellarmine attempted to defend Pighius' opinion, but he only qualified it as "probable" while admitting that it was not the common opinion.

The Decretists of the 12th and 13th centuries treated the questions of a heretical pope at length and proposed various ways of explaining how he could be judged and deposed.  None of them denied that a pope could fall into heresy.  Most mistakenly believed a pope could also be judged and deposed for notorious immorality.  Pope Innocent III rejected this opinion when he famously said he could only be judged by the Church for heresy.

The various theological opinions about loss of office for papal heresy are simply ways of explaining how a pope can be legally removed without the Church exercising authority over him.  None of the opinions, when correctly understood, support sede-vacantism. They all maintain that the pope must be legitimately deposed or declared deposed before he loses his authority and before the see becomes vacant.  

Now of course this is all irrelevant to you, as you said already that you believe Pope Benedict XVI was a heretic upon election, and it's canon law that a heretic cannot be elected Pope. Ergo, according to your own beliefs, BXVI was not the Pope.

The points that the sedevacantists make that are most compelling are Francis promulgating as "magisterium" in the AAS that public unrepentant adulterers can receive Holy Communion as well as officially changing the teaching of the Church to state that the death penalty is inadmissible due to human dignity. In addition, every Pope since Paul VI has officially legislated that it is permissible to give Holy Communion to Protestants and Schismatics in some capacity. It is hard to see how a true pope could legislate such immoral actions, not to even mention the errors and heresies of Vatican II. How can a pope, entrusted by God to pass on the true Faith to the faithful,  so brazenly infect the teaching authority of the church with such pernicious error that leads souls to hell? It makes no sense.

At a certain point, it seems the R&R approach guts the papacy as it allows for a man like Francis to hold the office. In this case, even if they do not admit we have no pope, the pope that they admit Francis is, is no pope at all as almost all of his teachings must be resisted and contradicted in order to keep one's Faith. This seems to me a tell tale sign that something is not right. God could never allow a notorious wolf to lead His flock in matters of doctrine.

Bad popes in the past were negligent, cowardly, or imprudent in their teaching office. And they personally committed various sins. But they never taught pernicious error to the flock ad nauseam like Francis. This puts the R&R'er in the position of saying that if a Catholic obeys the pope and believes his teaching, it actually damns him to Hell in the objective order.