The Pope gets involved openly backing one side or another in great power wars pretty much, never. They didn't even do this during the Thirty Years War! And there are good reasons for this. The Pope may have gotten involved in the various anti French Revolution coalitions, after all the French government was killing priests, but then they tried to work with Napoleon.
So this is one of those things that are not technically ASB, but you need a different curia and probably even a different Pope than Pius XII. There is a difference between the Axis friendly neutrality of Pius XII and openly getting involved on one side, which someone who had been high up in Vatican circles for most of his life would never do. There is also the problem that his predecessor had issued an anti-Nazi encyclical, again Pope really try to avoid doing a complete flip flop on past Vatican positions, again for very good reasons.
What I'm arguing is that the POD for this one may have to go back centuries before 1941, and it would have already resulted in a very different Catholicism.