Father Chazal is unquestionably a sedeprivationist ... whether or not he'd lay claim to the term.  He is NOT R&R. 

- It may be held that since the Vatican II popes possess a legal and valid election, they have a certain legal status as popes.
- It may be held that this legal status is sufficient to maintain the succession to Peter and the perpetuity of the hierarchy.

Nobody ever seems to explain to me how proper authority in the Catholic Church continues according to the strict sedevacantist position. I never get a clear answer.

Traditional Catholics have traditionally remained aloof and basically ignored "the man in a white cassock who lives in Vatican City".

Whether he is the pope, only legally the pope, or not pope at all doesn't really matter to us. In my opinion, that knowledge is AT LEAST morally impossible for 99.99% of men who weren't present at this or that secret meeting or election. For the average American or European living in 2018, no amount of study or thought is going to bring you to 100% certainty on the status of Pope Francis (and/or Pope Benedict).

But when I consider that the whole Crisis in the Church touches on God's secret plans and providence, which NO MAN IS PRIVY TO, nor has God shared his plans with anyone, it's even more impossible to know with certainty. I can't say "metaphysically impossible" because that would be like a plant having the use of reason. But it's morally impossible for 100% of men, not just the 99.99% who weren't intimately involved in papal elections, Fɾҽҽmαsσɳɾყ, etc.

Oh I've heard some good arguments in my time. From R&R, from conservative Novus Ordo, from sedevacantists, and from sedeprivationists. As you listen to any of their arguments, they sound quite convincing. Just one problem -- those arguments can't all be right!

They all sound convincing because they each focus on ONE ELEMENT of the mystery of the Crisis in the Church. If you focus on this element, you lean R&R. If you focus on this element, you lean sedevacantist. And so on. The problem is, NONE OF THESE POSITIONS ADEQUATELY ADDRESS ALL THE ISSUES AND OBJECTIONS INVOLVED. Hence my firm belief that we're dealing with a mystery.

But what we do know with certainty: We have to save our souls, and keep the Catholic Faith, and the man in white isn't promoting or protecting that Faith. On the contrary, he is doing everything he can to destroy it.

So we can pray for him, even in the Canon of the Mass (especially since he might be pope or legally pope -- who knows?) but that's about it.

We don't have to follow a material heretic, nor should we negotiate with him for "legitimacy", jurisdiction, approval, etc.

Previously, I posted excerpts.  Here's the complete text:

From Fr. Ringrose’s bulletin:
This feast reinforces Catholic teaching that Christ has given to Peter and his successors a unique role in the Church as Universal Pastor.  In this role as teacher Our Lord has promised that he who hears Peter hears him.  Recognizing this promise, the Church has infallibly taught that Peter and his successors cannot teach error to the Universal Church any more than Christ can.  So Christ guarantees that Peter will never teach error and Peter has the special assistance of the Holy Ghost to carry this out.
Last week we considered the error of sedevacantism, which holds that there is no pope, and that there is no hierarchy.  Today let us consider another error, referred to by some as “Recognize and Resist.”  In a nutshell, R&R holds that sometimes, the pope teaches error or imposes evil or harmful practices or laws.*  When he does, we must recognize his authority but resist his erroneous teachings or evil commands.  Good Catholics have mistakenly fallen into this error in their attempt to protect the teaching of the Church that the pope must have perpetual successors and that somehow there must always be a hierarchy.  The R&R position cannot be held because it ignores the clear teaching of the Church that the pope cannot teach error or impose evil or harmful practices and laws by virtue of the guarantee of Our Lord and the special assistance of the Holy Ghost.  If we recognize the pope’s authority to teach and rule the Church in matters of faith and morals, we have no choice but to assent and obey, for not to do so would be to fail to assent to Christ Himself, by Whose authority and in Whose name the pope speaks.  So R&R cannot be the answer, and like sedevacantism, it too must be rejected.
(*Some have said that the pope taught error at the time of St. Athanasius, but a closer examination of the facts shows this not to be true.)
 
From Fr. Ringrose’s posting in his church:
It is the teaching of the Church that the office of the Chair of St. Peter (Peter and his successors, the popes) is indefectible, that is it is always free from error and must be perpetual.  Its teachings are the standard and rule of Faith, despite the worthiness or unworthiness of the successor.  In light of this, what is a faithful Catholic to do?  Join or re-join the Novus Ordo?  By no means!  It is a false religion and to do so would be to abandon the Catholic Faith.
The question arises:  How is it that the New Order popes have attempted to impose on the Church erroneous teachings and harmful or evil law or practices?  Particular attention must be given to two of the most widely-held erroneous explanations:  sedevacantism and recognize and resist (R&R).  In light of what has been said, the following become apparent:
- Contrary to the teaching of the Church: The pope can teach error sometimes and impose harmful or evil practices and laws on the Universal Church.  The Faith requires all Catholics to reject this idea.
- Contrary to the teaching of the Church: There is no hierarchy whatsoever.  (It is de fide that the hierarchy must be perpetual.)  Therefore, Catholics must reject sedevacantism.
- Contrary to the teaching of the Church: We may resist the authority of the pope.  Therefore, we must reject R&R.
- Since it is obvious that the Vatican II popes have imposed teachings and practices contrary to Faith and morals, it must be concluded that the infallible and indefectible teaching power promised to Peter’s successors is absent.
- It may be held that since the Vatican II popes possess a legal and valid election, they have a certain legal status as popes.
- It may be held that this legal status is sufficient to maintain the succession to Peter and the perpetuity of the hierarchy.
It would appear, then, that the Chair is not totally vacant, nor is it completely full.  The new order popes possess some legal aspect as popes but lack the authority to teach or rule on matters of faith and morals.  In the face of this situation, the proper response of all faithful Catholics is to believe what Catholics have always believed and to do what Catholics have always done.  We cannot go wrong with that!