Considering that ZUN views Japanese culture as a natural evolution of other East Asian cultures (IIRC it was in the IN spellcard commentary, or an interview), I think that Buddhism and Daoism complements things in Gensokyo there. It doesn't matter that they aren't originally from Japan, really, provided that the local interpretation of such ideas fits the existing order well.
Now, adding Christianity to TH14's plot fits from historical standpoint, but for the actual religion, well, I'm not sure that Christianity's well-integrated in modern Japan, China, or Taiwan (Korea, however...a bit shocking if you ask me).