One of the parallels that MHFM points out between the Great Western Schism and the period after the death of Pius XII is that in both cases there is an antipope who took the name of John XXIII, who reigned from Rome and summoned a false council in the third year of his anti-pontificate. The parallel is striking. Perhaps you already noticed, but there are at least four other parallels between the two periods that in my opinion cannot be of coincidence:
Great Western Schism – «Were Urban now to succeed in creating an Italian majority in the Sacred College, the return of the Holy See to its dependence in France would be greatly deferred, if not indeed altogether prevented. [The King of France,] Charles V… secretly encouraged the Cardinals, promising them armed assistance… Confident in his powerful support, the thirteen Cardinals assembled at Anagni, on the 9th August 1378… declaring Urban’s election to have been invalid…» (Ludwig von Pastor, The History of the Popes, Vol. I, Book I, p. 126-127)
1958 Conclave – «On the fourth ballot, according to FBI sources, Siri again obtained the necessary votes and was elected supreme pontiff. But the French cardinals annulled the results, claiming that the election would cause widespread riots and the assassination of several prominent bishops behind the Iron Curtain [Communist Soviet Union].» (Paul L. Williams, The Vatican Exposed, Amherst, NY: Prometheus Books, 2003, pp. 90-92. quoted in: The Cardinal Siri Election in Brief )
Great Western Schism – «Great confusion was occasioned by a misunderstanding which occurred after the election. The crowd forcibly broke into the Conclave…» (The History of the Popes, Vol. I, Book I, p. 118)
1958 Conclave – «The scene around the Vatican was one of incredible confusion(…) The crowd waited in agony of suspense.» (The Houston Post, October 27, 1958, Section 1, pages 1 & 7.; quoted in: The Cardinal Siri Election in Brief )
Great Western Schism – «… the Cardinals, dreading to inform them [the crowd] of the election of Prignano [Urban VI]… persuaded the aged Cardinal Tibaldeschi to put on the Papal Insignia and allow the populace to greet him.» (The History of the Popes, Vol. I, Book I, p. 118-119)
1958 Conclave – «Clouds of smoke were caught in search lights trained on the Sistine Chapel chimney. ‘Bianco! Bianco!’ roared many in the crowd. ‘White, white.’ (…) Chigi… told newsmen later he would arrange to have the cardinals informed of Sunday’s smoke confusion in the hope that something can be done to remedy the situation Monday.» (The Houston Post, October 27, 1958, Section 1, pages 1 & 7)
Great Western Shism – «On the 20th September they informed the astonished world that the true Pope had been chosen in the person of Robert of Geneva, now Clement VII.» (The History of the Popes, p. 127)
1958 Conclave – «… but something strange had occurred inside the Sistine Chapel which prevented the newly elected Pope from appearing, and which left the crowd – and the waiting world – confused and bewildered. It was only two days later that Angelo Roncalli [John XXIII] was elected.» (MHFM — The Cardinal Siri Election in Brief )
I am almost sure that there are other parallels that could be identified, but the point is that, in my opinion, God allowed things to happen in such a way that the Great Western Schism would stand in history as a prefigurement of the Final Schism on the final days. And as the fulfillment is always greater than the prefiguration, while the latter was the Western Schism, the former is an almost universal one.
Also, these parallels, if really intended by God, further show that the false resistance groups like the SSPX are deluded and dead wrong in considering the Vatican II line of antipopes as the legitimate popes, by reason of their failure to understand the situation in which we are living that stems from their bad will. To be consistent, one must recognize that as in the Western Schism there was a line of antipopes, in the Final Schism there must be one also — and a worse one. Their false resistance will never bring good fruit because it is not founded in truth.