To include speculation as to why Nazis and not...
I think Hawkmoon was taking it in the right direction. Nazis are a modern, western, well documented evil whose crimes were enormous in scale, accomplished with industrial efficiency, widespread approval and meticulously recorded by the perpetrators. They are enough like us to elicit the horror of feeling associated with evil yet they tend to segregate themselves with pride. That self-inflicted separation makes them easier to vilify and compartmentalize. In their time they were a very real existential threat and were not easily defeated. Most viewers in the US grew up hearing stories from elders who personally fought against Nazis or at least spent their formative years consuming post-war fiction and histories that prominently featured the Nazi menace.
Further, and sort of playing on your point, Nazis (like Zombies) are safe enemy. There are no significant or accepted groups within modern culture who are offended by killing Nazis and folks all over the political map will unite in their hatred of Nazis.
So yeah, leftists in entertainment who hated that they smacked the Russians around probably contribute a little to the use of Nazis as bad guys. Probably quite a bit less so than the impact of Jewish writers or the simple fact that Nazis are - as Hawkmoon said - an easy, lazy, socially tuned shortcut for an enemy that you do not wish to have the audience feel sympathy for.
There are lots of nasty groups in history, some being awfully interesting.
No argument, but most are harder for an American audience to relate to. Americans either didn't fight them, fought them only indirectly, beat them handily, were unable to sufficiently publicize their crimes or simply don't feel the same connection to their atrocities because so much time has passed.
Or (crazy idea) some baddies not a carbon copy of an historical group?
That is particularly hard, but certainly a good goal for writers out there.