Having read everything Tolkien wrote many times through, it's hard for me to imagine how anyone could think it has an explicitly Christian theme. Influenced? I guess. As a product of his culture, Tolkien would be no more capable of writing a novel completely uninfluenced by Christianity then I would be, and I'm an atheist.
His friend CS Lewis shows us what a fantasy novel meant to be a Christian analogy would look like with his "The Lion, The Witch, And The Wardrobe."
Of course as a children's story, it hardly compares to the epic ring trilogy and all its backstory. I can't believe I just read a suggestion that "The Return of the King" is a Christ reference. I guess if you just look at those words you might think so, except that the Tolkien king in question plays no redemptive role for humanity, elves, dwarves, or for anyone else. His return in fact marks the beginning of a decline and eventual falling of his city and his house.
Meanwhile, as the king was returning to little avail, the world was actually being temporarily saved by someone completely different, and not by a king at all – well, by two somebodies, Frodo and Sam, though Frodo gets most of the credit. (And what a queer-coded couple they make! Sam's tender love for Frodo reads as all but explicitly romantic.)
Christian? The idea is laughable.