Answer: First, people need to understand what the teaching “No one can judge the Holy See” means. It comes from the early Church. In the early Church, when a bishop was accused of a crime, there would sometimes be a trial presided over by other bishops or by a patriarch of greater authority. These bishops would sit in judgment on the accused bishop. The Bishop of Rome, however, since he is the supreme bishop in the Church, cannot be subjected to any trial by other bishops or by other people.
Pope St. Nicholas, epistle (8), Proposueramus quidem, 865: “… Neither by Augustus, nor by all the clergy, nor by religious, nor by the people will the judge be judged… ‘The first seat will not be judged by anyone.’”
This is what “No one can judge the Holy See” means. It does not refer to recognizing a manifest heretic who claims to be the pope as one who is not a true pope. This brings us to the second point, which is the most important in this regard.
Second, the Holy See has told us that no heretic can be accepted as the valid occupant of the Holy See (the Pope)! With the fullness of his authority, Pope Paul IV declared that anyone who has been promoted to the Papacy as a heretic is not a true and valid pope, and that he can be rejected as a warlock, heathen, publican and heresiarch.
Pope Paul IV, Bull Cum ex Apostolatus Officio, Feb. 15, 1559: “6. In addition, [by this Our Constitution, which is to remain valid in perpetuity, We enact, determine, decree and define:] that if ever at any time it shall appear that any Bishop, even if he be acting as an Archbishop, Patriarch or Primate; or any Cardinal of the aforesaid Roman Church, or, as has already been mentioned, any legate, or even the Roman Pontiff, prior to his promotion or his elevation as Cardinal or Roman Pontiff, has deviated from the Catholic Faith or fallen into some heresy:
(i) the promotion or elevation, even if it shall have been uncontested and by the unanimous assent of all the Cardinals, shall be null, void and worthless; (ii) it shall not be possible for it to acquire validity (nor for it to be said that it has thus acquired validity) through the acceptance of the office, of consecration, of subsequent authority, nor through possession of administration, nor through the putative enthronement of a Roman Pontiff, or Veneration, or obedience accorded to such by all, nor through the lapse of any period of time in the foregoing situation; (iii) it shall not be held as partially legitimate in any way…
(vi) those thus promoted or elevated shall be deprived automatically, and without need for any further declaration, of all dignity, position, honour, title, authority, office and power… 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; (ii) the laity; (iii) the Cardinals [etc.]… 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).
10. No one at all, therefore, may infringe this document of our approbation, re-introduction, sanction, statute and derogation of wills and decrees, or by rash presumption contradict it. If anyone, however, should presume to attempt this, let him know that he is destined to incur the wrath of Almighty God and of the blessed Apostles, Peter and Paul.
Given in Rome at Saint Peter's in the year of the Incarnation of the Lord 1559, 15th February, in the fourth year of our Pontificate.
+ I, Paul, Bishop of the Catholic Church…”
Thus, one is obeying and adhering to the teaching of the Holy See in rejecting as invalid the heretical post-Vatican II claimants. They are not true popes, according to the teaching of the Holy See.
Third, it was near the beginning of this Bull, prior to the declaration that the faithful can reject as totally invalid the “election” of a heretic, that Pope Paul IV repeated the teaching that no one can judge the pope.
Pope Paul IV, Bull Cum ex Apostolatus Officio, Feb. 15, 1559: “1. In assessing Our duty and the situation now prevailing, We have been weighed upon by the thought that a matter of this kind [i.e. error in respect of the Faith] is so grave and so dangerous that the Roman Pontiff, who is the representative upon earth of God and our God and Lord Jesus Christ, who holds the fullness of power over peoples and kingdoms, who may judge all and be judged by none in this world, may nonetheless be contradicted if he be found to have deviated from the Faith.”
Unlike non-sedevacantists who use the “no one can judge the Holy See” argument, Pope Paul IV correctly distinguishes between a true Catholic pope, whom none can judge, and a manifest heretic (e.g. Benedict XVI). A manifest heretic has revealed himself to be a non-Catholic who is not the pope, since he is outside the true Church. This is striking proof that sedevacantists, who hold as invalid the “elections” of the manifest heretics Joseph Ratzinger, Jorge Bergoglio, etc., are not judging a pope.
Fourth, many of the people who defend the Vatican II “popes” by arguing “no one can judge the Holy See” are themselves guilty of judging the most authoritative actions of the men they claim occupy the Holy See. Many of those "traditionalists" reject Vatican II, the “canonizations” of the Vatican II “popes,” etc. That is a schismatic position. They reject the authoritative actions of that which they deem to be the Holy See. Hence, the errors and false doctrines in the universal and authoritative actions of the Vatican II antipopes prove that they do not, in fact, occupy the Holy See. They are not true popes but heretical antipopes.
 Denzinger 330.
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