Regarding the ancient discipline, which has been the subject of some posts above, Pope Pius XII expressly says that it has long been revoked, and that he has established the new discipline for the whole Church, which also takes its sanction from the faith laid out at the Vatican Council of the Supreme Pontiff's universal jurisdiction.
So due distinctions must be made. While in the first ages of Christendom, such consecrations were lawful under the positive law of the Church itself subject to the provisions made or consented to by the Roman Pontiff, today they would be lawful but only under epikeia in cases of necessity.
Malleus, it's only to be expected that we would differ in our application of the principles, otherwise there wouldn't be such a multitude of opinions. But so long as we agree on the principles, to me that's good enough. Obviously, I hope we've all considered our own position thoughtfully and prayerfully and hold it because we think, all things considered, it is the best explanation. We can't all be right, but at least we can all either be right or err in good faith.
I'll briefly mention why I consider my own position the most prudent with regard to the Arian analogy you bought up.
Does it matter if at the time of Liberias - Arian Bishops accepted him as a legitimate Pope? Obviously not because they themselves were outside the Church because they were Arian.
Agreed, and likewise those who fall prey to the prominent errors of our time, Bishop or Pope notwithstanding, will do so to their eternal peril. It matters not how numerous they are, some historians I've read said more than 90% of the Bishops fell into heresy here.
But this only undergirds my point. What did St.Athanasius, the hero of this time, do? He wasn't interested in condemning the Pope nor declaring the See of Peter vacant. Rather, he kept the faith and it alone and did not pass judgment. There were others who did, and I do not blame them, and after all these were not ordinary laymen but the Roman clergy, but these certainly did not help resolve the crisis nor even to tide it over in anyway, and certainly not as St.Athanasius courageously did, and these latter even may have contributed to its complication.
I gave another example. St.Maximus and Pope Honorius. A letter this Pope wrote to the Patriarch Sergius led to the Monothelite heretics being confirmed in their errors. When St.Maximus, who understood the underlying doctrine with a profundity and a purity that I'm convinced would entirely surpass ordinary men, had holy Mother Church not later defined it herself, was forced to agree with the Pope (or so they thought at least) or to condemn him, he did neither, but only held to and expounded the true doctrine in question, that in Christ there are two principles of operation of the will, proper to his divine and to his human nature respectively and properly so called. Then the Greeks cut out his tongue and killed him, though today they venerate him as a Father of the Church.
May it please God to restore Christendom to her former greatness and glory, and, even, as Our Lady has promised, to heights greater still.