I've long thought that a pro-Nazi pope leading to a schism during World War II would be interesting. Perhaps the POD is something in the Lateran Treaty that gives Mussolini influence over the papacy.
The entire point of the Lateran Treaty was to give enough indipendence to the Pope that he'd lift all proclaims against partecipating in Italian politics (and, by extension, supporting the Italian Government at that point in time: that is to say, at that time, Mussolini), there's no way the Pope would accept such a clause being inserted, simply because he's the party that has nothing to lose by saying "no".
As for the thread question: one consequence, aside from giving only token protest to Nazi Germany'0s treatment of the Catholic Church in Poland, would be that Rome's Jeish community would be even more screwed, as there's no way TTL's Pope would try and hide any in the Vatican (in fact, he'd likely get the clergical machine working to point out as many as possible). Meaning that the Fosse Ardeatine get even more filled with corpses; and in the post-war, there's going to be some pretty awkward questions going around the city of Rome, if not the whole of Italy. I certainly don't expect Romans to see this Nazi Pope in any favourable light whatsoever even if the WAllies and Italian governments combined swept him away and pretended that he never happened.
External reactions aren't my forte, but it wasn't long ago that US Catholic discrimination had subsumed into politer forms. Even if bishops from the Americas convened in Monreàl or New York or whever to elect an antipope ideologically opposing the then-reigning pope, I can't imagine the situation looking good for US atholics. LAtin Americans might just nod and grin and pretend to not to hear the whole way through, though.