I always saw more parallels to Norse mythology, myself. Pretty much all the characters relate back to some Scandinavian myth or other. The only possibly Christian idea I ever saw was the idea of dying for something greater than yourself, but even that isn’t specifically Catholic at all.
I thought you’d left. I like the new tagline!
You missed details such as the Ring’s being destroyed on the date of the Annunciation, and some lines that are almost word-for-word from the Bible. However, you’re right that all great striving and sacrifice is universal, not necessarily specifically Christian.
Gandalf’s sacrifice and “resurrection” separate it from other mythologies. The influence of the Norse can’t be disregarded; “Isengard” isn’t far off from “Asgard”.
I thought that was a bit strange, since what motivated Tolkien was the fact that England itself didn’t have as many myths & legends as other cultures had. While acknowledging the Arthurian legends, he seemed to feel they were somewhat lessened by the fact that they are set in Christian England (and thus more recent).