Cincinnati Archbishop John Baptist Purcell
Addressed the issue on the papacy at the First Vatican Council
1. The First Vatican Council declared “this See of St. Peter always remains unimpaired by any error.” 
The fathers of the First Vatican Council found forty papal errors before declaring the See of Peter always remains unimpaired by any error. The context of the council’s declaration concerns salvation by adherence to the teachings of the Catholic Faith, which includes theological conclusions, dogmatic facts, declarations, definitions, condemnations, laws, and disciplines. However, theological opinions are not part of the Catholic Faith and popes can err in opinions where the Church hasn’t made an official pronouncement.
For instance, in 1336 AD, Pope Benedict XII officially defined that the blessed souls of the dead “see the face of the triune God immediately after death.” However, in a homily five years earlier, Pope John XXII taught the blessed souls do not attain the Beatific Vision until after the General Judgment. This only constituted a theological opinion in his day because the particular judgment had not yet been defined. Therefore, Pope John XXII erred, but not against the Catholic Faith, which defined the teaching after Pope John’s death. The First Vatican Council certainly recognized how John’s erroneous theological opinion didn’t deny a formal Catholic teaching, thus John’s pontificate was truly unimpaired by any errors against the Catholic Faith.
Since popes always remain unimpaired by any error against the Faith, they need never to be judged, warned, or declared to have gone against the Faith. Those who argue that such a pope would need to be warned assume that a pope can be impaired by error in order to be warned. This theological opinion, found in the teachings of John of St. Thomas, Cajetan, and Suarez, is now considered heresy by the First Vatican Council’s declaration. If ever a pope should publicly go against the faith, he would lose his office at the moment of his error since he can’t err and remain pope at the same time. As seen in footnote , Vatican I taught in the address about the pope:The Church would not be, for a moment, obliged to listen to him when he begins to teach a doctrine the Church knows to be a false doctrine, and he would cease to be Pope, being deposed by God Himself.
Those who argue that a declaration is needed before the faithful are to ignore, resist, or reject the fallen pope assume either the faithful are to be in union with an antipope until a declaration, which is absurd, or that a defected pope remains pope until the declaration, which is a blunt denial of Vatican I and the Catholic Faith.
Since the Vatican 2 popes are impaired by errors against the Catholic Faith , they can’t be true popes, or the First Vatican Council is wrong and the Catholic Faith is just another false religion.
All so-called traditionalist Catholics, such as the SSPX, and their publications and websites, such as The Remnant, Catholic Family News, and Tradition in Action necessarily reject the Catholic Faith, and the infallible teaching of the First Vatican Council’s declaration that the See of St. Peter always remains unimpaired by any error.
 Vatican I declared, “For the fathers of the Fourth Council of Constantinople, following closely in the footsteps of their predecessors, made this solemn profession: ‘The first condition of salvation is to keep the norm of the true Faith. For it is impossible that the words of our Lord Jesus Christ Who said, ‘Thou art Peter, and upon this rock I will build my Church’ (Matt. 16:18), should not be verified. And their truth has been proved by the course of history, for in the Apostolic See the Catholic religion has always been kept unsullied, and its teaching kept holy.’ …for they fully realized that this See of St. Peter always remains unimpaired by any error, according to the divine promise of our Lord and Savior made to the prince of his disciples, ‘I have prayed for thee, that thy faith may not fail; and do thou, when once thou has turned again, strengthen thy brethren’ (Luke 22:32)
So, this gift of truth and a never failing faith was divinely conferred upon Peter and his successors in this chair, that they might administer their high duty for the salvation of all; that the entire flock of Christ, turned away by them from the poisonous food of error, might be nourished on the sustenance of heavenly doctrine, that with the occasion of schism removed the whole Church might be saved as one, and relying on her foundation might stay firm against the gates of hell.”
The topic of a pope becoming a heretic was addressed at the First Vatican Council by Archbishop Purcell, of Cincinnati, Ohio: “The question was also raised by a Cardinal, ‘What is to be done with the Pope if he becomes a heretic?’ It was answered that there has never been such a case; the Council of Bishops could depose him for heresy, for from the moment he becomes a heretic he is not the head or even a member of the Church. The Church would not be, for a moment, obliged to listen to him when he begins to teach a doctrine the Church knows to be a false doctrine, and he would cease to be Pope, being deposed by God Himself.
“If the Pope, for instance, were to say that the belief in God is false, you would not be obliged to believe him, or if he were to deny the rest of the creed, ‘I believe in Christ,’ etc. The supposition is injurious to the Holy Father in the very idea, but serves to show you the fullness with which the subject has been considered and the ample thought given to every possibility. If he denies any dogma of the Church held by every true believer, he is no more Pope than either you or I; and so in this respect the dogma of infallibility amounts to nothing as an article of temporal government or cover for heresy.” (The New Princeton Review, Volume 42 p. 648, also The Life and Life-work of Pope Leo XIII. By James Joseph McGovern p. 241)
 Many examples can be provided to establish the fact that Vatican 2 popes are impaired by errors against the Catholic Faith. However, the following two suffice:
[a.] The Church of Christ is not one in Faith…because the Church of Christ and the Catholic Church are not one and the same thing. False religions and their members form part of the Church of Christ in the external forum. For example: The 1993 Balamand Statement approved by John Paul II on May 25, 1995, in Ut Unum Sint, n. 59, declared:
13. In fact, especially since the panorthodox Conferences and the Second Vatican Council, the re- discovery and the giving again of proper value to the Church as communion, both on the part of Orthodox and of Catholics, has radically altered perspectives and thus attitudes. On each side it is recognized that what Christ has entrusted to his Church – profession of apostolic faith, participation in the same sacraments, above all the one priesthood celebrating the one sacrifice of Christ, the apostolic succession of bishops – cannot be considered the exclusive property of one of our Churches.
14. It is in this perspective that the Catholic Churches and the Orthodox Churches recognize each other as Sister Churches, responsible together for maintaining the Church of God in fidelity to the divine purpose, most especially in what concerns unity. According to the words of Pope John Paul II, the ecumenical endeavour of the Sister Churches of East and West, grounded in dialogue and prayer, is the search for perfect and total communion which is neither absorption nor fusion but a meeting in truth and love (cf. Slavorum Apostoli, n. 27).
[b.] Communicatio in Sacris is condemned by Sacred Scripture and runs contrary to the divine law, which is why the Catholic Church has many times proscribed interreligious worship through law and decree as being an abomination (like Benedict XVI worshipping with Muslims in a Mosque and with Lutherans in Lutheran churches, John Paul II worshipping with a Zoroastrian priestesss in 1986, and Francis I worshipping with Jews, Muslims, Protestants, etc.). The Second Vatican Council, nevertheless, approves and encourages joint religious events, while the conciliar popes made ecumenism a priority of the highest order and took such great pains to showcase before the whole world events like Assisi I, II, and III. The latest Assisi Events in 2011 exhibited a Voodoo warlock singing to the goddess Olokun in front of an altar in a Catholic basilica. Following the customs of Voodoo possession, the warlock asked to be possessed by the goddess.