No question that there are doctrinal differences between denominations. Eastern Orthodoxy, Roman (Curial) Catholicism, Protestantism with their sub-groups (all of which, btw, would probably have bee considered heretical by the original followers of Jesus centered around the Twelve Apostles); Sunna and Shia (and sub-groups) in Islam; Theravada, Mahayana, Tibetan (and sub-groups) in Buddhism; and never mind the variations in Hinduism.
I do not doubt, as you pointed out, that JRRT was convinced, probably rightly so, that his writing was consistent with Roman Catholic doctrine of his time (the Second Vatican Council was still about seven years in the future when RoTK was published), other Christian denominations, and never mind non-Christian beliefs, having no influence. Where I think he erred,
if he assumed parts of that doctrine to be exclusively RC (I don't know that or where he ever stated this so explicitly), is in this exclusivity. You mentioned Anglicanism; I've read a description of High Anglicanism being basically RC, just without the pope; perhaps so. I am assuming that the implication of exclusivity derives from his use of the word "fundamentally" in Letter #142 dated 02 December 1953 to Father Robert Murray, S.J., who had read parts of LoTR before its publication. Religions, like their secular counterparts political parties, compete with each other, and both need to emphasize the
differences to their competitors in striving to gain followers, declare these differences to be fundamental and exclusive to their own specific "party"; and it goes almost without saying that each "party" considers their difference to be good.
I just thought of
the one scene in LoTR which comes closest (on the good side) to a religious ritual: chapter V "The Window on the West" in Book Four in TT:
"Before they ate,
Faramir and all his
men turned and faced west in a moment of silence. Faramir signed to
Frodo and
Sam that they should do likewise.
'So we always do,' he said, as they sat down, 'we look towards
Númenor that was, and beyond to Elvenhome that is, and to that which is beyond Elvenhome and will ever be. Have you no such custom at meat?'"
Would you say that this scene contains anything exclusive to Roman Catholic belief, absent from or even contradicting beliefs of other Christian denominations?