"I'm going out on a limb and speculating that Satan implemented Benedict XV as anti-pope to sow the seeds of Vatican II in the Church, and then allowed Pius XI and Pius XII to reign in order for a modernist under-current to grow strong, all the while the Church looked perfectly healthy because Pius XI and XII were seemingly orthodox popes in order to deceive the world."
You don't become an anti-Pope by paving the way for a takeover of the Church. You don't even become an anti-Pope by having an invalid election, because if the world approves of someone as Pope, they're Pope until proven otherwise, such as through being a pertinacious and manifest heretic.
If Catholics were getting sound Catholic doctrine from Benedict XV-Pius XII, no matter if they were appointing modernist cardinals or whatever, they were Popes. In the public forum they said nothing that should make us think otherwise -- except that of course Benedict XV issued the book of Canon Law that is pro-BoD, making him an anti-Christ to certain segments of the population.