First, we must address a common argument against judging the man who claims to be pope as a heretic. It goes something like this: "The pope has no superior on earth, and can be judged by no one."
This statement as it stands, is absolutely true. So why do sede vacantists believe that they can judge the man who sits on the chair in the Vatican an antipope?
It is useful, for better assimilation of the current discussion, to read also the article entitled "Judge not, that you may not be judged!".
In St. Matthew's Gospel, when the Lord Jesus Christ says: "Judge not, that you may not be judged," is he in fact telling us to refrain from all judgment? No. All a person needs to do, is read the next four verses.
"For with what judgment you judge, you shall be judged: and with what measure you mete, it shall be measured to you again. And why seest thou the mote that is in thy brother's eye; and seest not the beam that is in thy own eye? Or how sayest thou to thy brother: Let me cast the mote out of thy eye; and behold a beam is in thy own eye? Thou hypocrite, cast out first the beam in thy own eye,"
So it is obvious that the Lord was prohibiting people from judging hypocritically, that is, of condemning others for sins that we are guilty of ourselves. And how does the Lord finish His thought? With these words: "and then shalt thou see to cast out the mote out of thy brother's eye."
So he is not telling us to refrain from judging at all. He is merely telling us that we have to accuse, judge and correct ourselves, and then shall we see to judge others. In other words, judging others is not forbidden, judging them hypocritically is.
Type of judgment
There are two types of judgment. Juridical, which comes from authority, also called canonical judgment; and epistemological judgment.
Epistemology is the study of knowledge, that is; the study of what we know, and how we know it. Naturally since most sede vacantists are simple lay people, they are not authorized to judge anybody canonically (for the purpose of imposing penalties, etc.), though as we have heard from the mouth of God Incarnate, once we have purified ourselves of our own sins, we shall then see clearly enough to notice and admonish the sins in others.
"Judging the pope?" Or a man already judged?
Now, we still haven’t solved the problem of "judging the pope". We know that he is judged by no one on earth. This means that when he exercises his authority, there is nobody superior to him on earth and therefore nobody can overturn his decrees.
When we speak of judging someone to be an antipope, there are there are three things to be distinguished;
1) the papal authority
2) the person of the pope
3) the union of the papal authority with the person
The papal authority is from God, yet the union of this authority with the person is made by human election. The papal authority in and of itself can never be judged by any man and neither can any act or decree, which proceeds from this authority.
The person who would be elected pope, however, is indeed judged by his superiors, who constantly promote him from deacon, to priest, to bishop, etc.
When this person has been judged by enough Cardinals to be elected pope, there has been still no judgment of the papal authority, but rather of the person, using the dogmas of faith and morals as a guide in determining that this person is indeed worthy to be united to the papal authority.
But if the person of the pope (or anybody) were to publicly fall into heresy, he would no longer be in the Catholic Church, because it is Catholic dogma that heretics are outside the Catholic Church:
Pope Eugene IV, the Council of Florence, ex cathedra: “It (the Holy Catholic Church) firmly believes, professes and preaches that all those who are outside the Catholic Church, not only pagans but also Jews or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels.”
Strong and beautiful words from Pope Pius IX, reiterating and confirming the infallible decree of Pope Eugene IV, but from the other side, professing what is necessary to be counted among the sons and daughters of God, namely the divine and Catholic Faith (and not to reject any point thereof). People who do so are to be avoided, as testified by the constant Tradition of the Church, teachings of both the Ordinary and Extraordinary Magisterium and even Scripture. In the Epistle to Titus, St. Paul admonishes the faithful as follows: “A man that is a heretic, after the first and second admonition, avoid: Knowing that he, that is such an one, is subverted, and sinneth, being condemned by his own judgment.”
St. Matthew 16:18-20: "And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it. And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose upon earth, it shall be loosed also in heaven. Then he commanded his disciples, that they should tell no one that he was Jesus the Christ."
Pope Paul IV, Cum Ex Apostolatus Officio: "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 fulness 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 [...] and We have been concerned also lest it may befall Us to see the abomination of desolation, which was spoken of by the prophet Daniel, in the holy place..."
"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;
"(iv) to any so promoted to be Bishops, or Archbishops, or Patriarchs, or Primates or elevated as Cardinals, or as Roman Pontiff, no authority shall have been granted, nor shall it be considered to have been so granted either in the spiritual or the temporal domain;
"(v) each and all of their words, deeds, actions and enactments, howsoever made, and anything whatsoever to which these may give rise, shall be without force and shall grant no stability whatsoever nor any right to anyone;
"(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: the Cardinals, even those who shall have taken part in the election of this very Pontiff previously deviating from the Faith or heretical or schismatical, or shall otherwise have consented and vouchsafed obedience to him and shall have venerated him;
"Castellans, Prefects, Captains and Officials, even of Our Beloved City and of the entire Ecclesiastical State, even if they shall be obliged and beholden to those thus promoted or elevated by homage, oath or security; 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)."