What he said. What's the explanation? Nazis experimenting with magic, thus causing a magical arms race?
World with a publicly known but low level of ambient magick. As mentioned, the US until the Wyrd War limited itself to a Militant Chaplain Corps (non-denominational) who practiced a form of theurgy.
I'll post the images of other countries sorcery services eventualy including the NS-ZaubernKorps (National-Socialist spellcasting corps).
Also, what's with the Christian Fundamentalists? In OTL, the fundamentalist movement wasn't that influential (and roundly mocked after the Scope "Monkey Trial" of 1925) until the 'sixties, when the Moral Majority and Billy Graham took off in reaction to Communism and the counterculture [waits breathlessly for someone to correct his surmise].
I did not mean big "F" fundamentalists (in the sense of an organised movement) just the types that take quite litteraly Exodus 22:18 about "not suffering a witche to live" and other parts about "proper christian behaviour". Seemed to be a fair bit of those back in the days
If you prefer, replace that bit with "realy, realy conservative christians from our modern point of view".