Tolkien’s work: Is it Christian allegory or pure fantasy?

Fantasy. He said so himself.

Read his letters. He's stated that he doesn't like allegory and he wanted mythology for England free of christian influence. One of his hangups with Arthurian legends is they're influenced by christianity.

"You read Tolkien and there’s times where it feels infused with an almost scriptural kind of feeling," [Rings of Power showrunner J.D. ] Payne told the Deseret News, adding that Tolkien’s work "feels deeply influenced by sort of a wisdom tradition"

Ah yes, the old "sort of a wisdom tradition". This is exactly the level of insight I expect from the producer of Rings of Power. :)

LOTR is religious in the sense that there is a right thing to do and a wrong thing to do, and doers of good things prosper while doers of bad things suffer. Fantasy, in other words.

The only slightly-Catholic bit is that wrongdoers don't necessarily suffer at the hands of others (though there is certainly a lot of that) but that doing wrong is a psychic punishment in and of itself. Gollum, Denethor, even Saruman by the end all were mostly tortured by their own thoughts. In other words, doing the right thing has nothing necessarily to do with others -- it's simply the only healthy way to live.