4.15. What about the Vatican II popes — aren’t they the legitimate successors of St. Peter?
No. While they may have been material claimants to the papacy, they could not be formal popes, because a manifest heretic cannot be pope. This is the unanimous teaching of saints, doctors, canonists, and theologians.
Pope Paul IV’s 1559 bull Cum ex Apostolatus Officio teaches that even if a man is elected pope by all the cardinals, his election is null and void if he had previously deviated from the faith.
The Vatican II popes — from John XXIII to Leo XIV — publicly taught heresies (e.g., religious liberty, false ecumenism) and promoted sacrilegious disciplines, which is incompatible with holding the papal office.
Further reading:
Paul IV's 'Cum ex Apostolatus' on a heretic pope: Text and commentaries by The WM Review