On the Incompatibility Between Clerics and Demi-humans

I was musing about the lack of religions in Tolkien last night, and I happened to think about two kinds of fantasy. In The Lord of the Rings you have a single Demiurge, Eru Ilúvatar, and several Minor Deities, the Ainur, including Morgoth, the Enemy. The parallel with the Judeo-Christian tradition is pretty evident – God creates the world, one of the Angels betrays him and the traitor falls. Anyway, there are many other elements that make Tolkien's Middle Earth pretty much unique, and far from the Judeo-Christian tradition: the first is that no choice of faith has to be made (the deities live on Arda, if you trust the elves), the second is that The Enemy is just as real as me and you. Supposing Tolkien's Middle Earth is our earth before the Age of Men, everything makes sense: as soon as the elves leave the world humans have to make a choice of faith, because they have no more proof. Moreover, the people of Middle Earth are aware that the Ainur won't help them anymore (the reason is told in The Silmarillion), and you find that there is not a single prayer nor a curse to the gods in the whole novel.

In other fantasy works, where you have no demi-humans (for example Lady Hawk, Orlando Furioso or classic mythology, just to name a few), men tend to actively worship god or a pantheon of gods. This makes perfect sense, because the need of faith is undoubtedly a natural feature of men.

What I really dislike is the promiscuity between those two genres as it has been presented in the old editions of D&D, i.e. pagan priest casting bible miracle-like spells (Part Water, Create Food and Water, Walk on the Water and so on) in a world where magic, elves, dwarves and hobbits live toe to toe with humans. Does this make any sense at all? I'm not saying I don't like paganism in D&D (as a matter of fact, I like it very much!), nor am I saying that I dislike demi-humans, but I can't just stand the mismatch.