The Satanic Panic would probably be different in a US/Nazi Cold War, but then, so would a lot of things.
Assuming the victorious Nazis kept on with their occultic preoccupations(my understanding is that, OTL, their interest was rather limited, and Hitler even made fun of some of it), yeah, that could dovetal nicely with the agenda of occultophobic Christians in the 80s and 90s. The daycare panics could be spiced up with allegations that the abuse was being conducted as part of magic experiments ordered by Berlin("You think it's just a coincidence they're called kindergartens??"), and the smalltown incest cases could be focused on accusations against German-American families.
ON THE OTHER HAND...
Just as, during the real Cold War, far-left opinion tended to shade toward the pro-Soviet(eg. Henry Wallace, later on Angela Davis etc), I wonder if Christian fundamentalists in the ATL would be pro-Nazi, and hence ignore or at least downplay the more counter-Christian aspects of their hero regime. Sorta like how the free-wheeling western bohemians who proclaimed themselves Communists managed to not notice that most Communist regimes were about as culturally and morally liberal as your average John Birch chapter.