Fr. Hesse:

Objective (or Material) heresy is: "According to the Church, salvation is attainable outside the Church".
Formal (or Manifest) heresy is: "I don't care what the Church teaches, the Church is wrong, I say salvation is attainable outside the Church".

The accusation that the conciliar popes are manifest heretics has never been proven.

What is "proven" is that the Papal Magisterium cannot ever become substantially corrupt, and that the Pope cannot promulgate a harmful Rite of Public Worship that displeases God.  To say otherwise is heretical.  You can come up with with whatever explanation you want for how it wasn't legitimate Papal Authority exercised freely that gave us the evils of V2 and the NOM, but to deny the above proposition is heretical.  You have been admonished publicly for this heresy multiple times, and yet you pertinaciously adhere to it.  That would make you a public/manifest heretic as well.

a corrupt Magisterium in these latter days

And I'm going to keep writing it until some of you wake up to the fact that you've completely (and pertinaciously) embraced a heretical ecclesiology.

This is not rocket science.  Our Lord promised the assistance of the Holy Spirit to the See of Peter, an assistance which prevents it from corrupting faith or morals.

You have two choices to avoid heresy, 1) claim that faith and morals haven't been corrupted (that V2 was misinterpreted by Modernists and the NOM is not essentially bad but has been abused) or 2) assert that legitimate Papal authority exercised freely did not produce V2 and the NOM.

Within #2, you have various choices, from sedevacantism, sedeprivationism, sedeimpoundism, Siri thesis, blackmailed pope, drugged pope, pope replaced by a double, etc.

This Chair of Peter cannot fail, and to say otherwise is heretical.  Period.  End of Story.  Address it with #1 or with #2 (and any permutation of #2), but you can't simply run off and pertinaciously embrace some repackaged form of Old Catholicism / Eastern Orthodoxy / Protestantism.

You have the temerity to refer to this Basic Foundation of Catholicism as "delusion".  Unbelievable.

There is another way. It is the way of Archbishop Lefebvre. Here's an article from the Dominicans of Avrille regarding the errors of both modernism and sedevacantism, which includes the stance of +ABL. Here's a quote from the article:

"Currently, facing a crisis in the Church, there are two errors to avoid: modernism (which, little by little, makes us lose the faith) and sedevacantism (which leans towards schism). If we want to remain Catholic, we must pass between heresy and schism, between Scylla and Charybdis."

Little Catechism on Sedevacantism - PART I - Dominicans of Avrille, France (dominicansavrille.us)

From the article (which I have been trying to explain to Mr. LaRosa since p.2 of this thread):

"If a Catholic were convinced that John Paul II (or another Pope after Vatican II) is a formal, manifest heretic, should he then conclude that he is no longer pope?

No, he should not, because according to the “common” opinion (Suarez), or even the “more common” opinion (Billuart), theologians think that even a heretical pope can continue to exercise the papacy. For him to lose his jurisdiction, the Catholic bishops (the only judges in matters of faith besides the pope, by Divine will) would have to make a declaration denouncing the pope’s heresy.

Now, in so serious a matter, it is not prudent to go against the common opinion.

But how can a heretic, who is no longer a member of the Church, be its leader or head?

Fr. Garrigou-Lagrange, basing his reasoning on Billuart, explains in his treatise De Verbo Incarnato (p. 232) that a heretical pope, while no longer a member of the Church, can still be her head. Indeed, what is impossible in the case of a physical head is possible (albeit abnormal) for a secondary moral head. “The reason is that – whereas a physical head cannot influence the members without receiving the vital influx of the soul – a moral head, as is the [Roman] Pontiff, can exercise jurisdiction over the Church even if he does not receive from the soul of the Church any influx of interior faith or charity.”

In short, the pope is constituted a member of the Church by his personal faith, which he can lose, but he is head of the visible Church by jurisdiction and authority that can co-exist with heresy.

To say that the bishops can judge the pope, if he is in fact the pope, is heretical.

Incorrect: As has been discussed in this thread, the pope can be the subject of a discretionary judgment, but not a coercive judgment.