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."