The polytheism isn’t, actually. Have you read The Silmarillion? Not really my favourite, but it does make the theology behind LOTR much more understandable. Basically, the universe is created by Eru - ‘the One’ - who then creates a number of great spirits, like Varda (Elbereth Gilthoniel) and Melkor, who turns evil (he’s the Satan figure). These are equivalent, sort of, to archangels, but act as demiurges - that is, they make the earth in accordance with Eru’s design.
What Tolkien said was that his universe, with Middle Earth, was not meant to be an alternative explanation for reality, but an account of the universe and of God which would be consonant with natural theology before any revelation (to Abraham, Moses or, of course, in our Lord). He is not trying to supplant revelation!
Sue