5) To better appreciate why Billot et al. are right, we need to consider the logic of why they say that universal acceptance is an infallible sign of the truth of a papal claim. The pope is the fountain of infallibility for the Church, and all "other" infallibility springs forth from him. If a man pretends to be pope (and isn't) and the Universal Church doesn't notice, then the universal Church, in principle, may learn false doctrine from him, and in principle, may defect. Which is an impossibility per the Divine Law. So it follows, given her indefectibility, that the universal Church will never accept a false pope. And to this day, she hasn't. And never will.
If Cardinal Billot is right; then a separatist R&R position falls like domino pieces, because if the elected Pope is indeed the fountain of infallibility for the Church, then there is an
obligation for all the faithful to loyally adhere to his rule and teachings. Catholicism 101.
Cardinal Billot From "De Ecclesia Christi":
“At the minimum one should firmly hold as absolutely unshakable and beyond all doubt the opinion that the adherence of the universal Church is always for her the one infallible sign of the legitimacy of the person of the Pontiff, and hence the existence of all the conditions required for this legitimacy. And one does not have to search far and wide to find reasons for this. It derives directly from the infallible promise and providence of Christ: The Gates of hell shall not prevail against her, and again, I shall be with you till the end of days. In point of fact, it would be one and the same thing for the Church to adhere to a false pope as it would be for her to follow a false rule of faith, because the Pope is the living rule of faith which the Church is obliged to follow in believing, and certainly this is always the case, as will appear most clearly from what we say below. God can certainly permit that on occasion the vacancy of the Holy See should persist for a long time. He can also permit that a doubt could arise about the legitimacy of a given person who was elected. But He cannot allow that the entire Church would accept as a true Pontiff one who is not truly and legitimately such.”
But also consider this, from the beginning, a fringe of Traditional Catholics, this is, a part of the universal Church has not recognized the conciliar popes as true popes because they have not followed them in word or action (they have not adhered to them since they are not in formal communion and in fact, are instead in state of
opposition towards them). According to Billot, this would be proof right there that the conciliar Popes are no true Popes, otherwise, everyone had recognized them as such; but not everyone did and has remained so, following Vatican II Council.
On the other hand, if Cardinal Billot is wrong, then there is a possibility that even if in the first years after the Council the entire Church seemed to have recognized the legitimacy of these popes, the legitimacy was not real on account of formal heresy prior to the elections, following the dogmatic principles lined in
cuм Ex Apostolatus. The fact that the entire Church (thousands of bishops) also accepted and went along with the Vatican II reforms also would mean little simply because of this gem:
All the bishops IN THE ABSENCE OF A POPE ARE NOT infallible.