Correct. JRRT's
middle-earth was also influenced by his professional area of expertise: Beowulf, the Norse (mainly Icelandic) Eddas and Sagas, some parts of the Arthurian legendarium, ... more personally by his fascination with the Finnish Kalevala, very likely Celtic influences of both Welsh and Irish origin, and even the odd bit of 20th century literature. He might have had very limited sympathy, if at all, for the Venerable Bede's (7th/8th century) contemptuous snort "What has Ingeld to do with Christ?", which could have led to the destruction of several stories similar to the practically sole survivor, Beowulf.
A
nd as I've posted before, even JRRT himself may have made the error of considering some trains of thought, of ethics, morals ... to be exclusively Roman Catholic. Seriously wrong as far as other Christian denominations are concerned, wrong to various degrees about the other two "Abrahamic" beliefs go, and even wrong for some non-"Abrahamic" belief systems. Here I mean what the respective theologians have worked out, not what the mass of the respective believers actually practice; that can have surprisingly little overlap.
I've given that observation no little consideration (and you aren't the first to posit it); to wit, why would JRRT limit his statement to just Roman Catholicsim to influencing his writing? Why not (as CS Lewis does in his works ) say that Christianity (or Christian Doctrine ) influenced his writing?
I've come up with a few answers that I think are plausible, but I have no way of verifying them (except that I know Catholic doctrine pretty well inside out).
1) This one I think is the most plausible: That JRRT being both very intelligent and , very well read (especially in western civ history and lit) knew that there are fundamental theological differences between Roman Catholic doctrines and Protestant Doctrines, most especially concerning fallen human nature and redemption. To be sure, there are differences among Protestant religions as well, most specifically regarding those two doctrines.
Calvinism (AKA today Presbyterianism) teaches something wholly different about sin (fallen human nature) than does RC and Lutheranism and Anglicanism.
Anglican doctrine** is the closest to RC teaching (nigh on identical), but Lutheran doctrine is a little different, lying somewhere between Calvinist doctrine and RC doctrine.
**If JRRT hadn't been Catholic I would put all my money on his having been Anglican
2) Having been raised in the RC church in the early 20th C. he may have learned that all Protestant religions deviated from Catholic teaching;
i,e, "got it wrong"
To be a Christian was synonymous with being a Catholic. To be anything else was at best to be "in error", at worst, to be a heretic.
If that is what he believed it is understandable that he would say his work is fundamentally a Catholic story; he was saying that his work was fundamentally Christian (Christian =Catholic, Catholic=Christian). But he also would know, as his priest/guardian/mentor would have undoubtedly taught him, that all those other religions, though not completely 100% Christian do get some it right (Doctrine of Trinity, Genesis, Escahtology etc). yet there are fundamental errors. He certainly would know that there is the Catholic Bible and the Protestant Bible (Catholic one containing seven more
books in the NT than the Protestant one).
So (1) and (2) are closely related differing only in that in (1) he intellectually acknowledges the the differences between RC doctrine and Protestant doctrine, and (2) he does kind of knee-jerk rejection of Protestant doctrine.
I think (1) is more like to have been what he was thinking.
3) As to his view of the contributions by the non-christian religions; e.g., Islam, Buddhism, Hinduism, Confuscianism etc., I can only speculate. JRRT was a kind man, a good man. I would bet he recognized some good in Islam and all "pagan" religions. He could see, much as his friend CS Lewis saw, that all religions have some form of the Tao in their moral codes (Tao= Golden Rule). But many of the doctrines of Islam , not to mention those of the other religions, are anithetical to Christianity, or especially to RC. So there would have been no reason (imo) for him to have acknowleged their influence or contribution.