I can see where this topic could easily lead us into murky waters, so I'll do my best to express my opinion without treading on any toes.
As JRRT wrote in several
places, he hated allegory and wished in no way for his new mythos to resemble Christianity. Since he was versed in many different mythologies, their influence can be readily picked up on by those who have studied different belief systems.
It always seemed to me that in his stories he seems to place a greater emphasis on a type of predestination (i.e.
Gandalf telling
Frodo that
Gollum may yet have something to do that shouldn't be hindered). Also, while it may be vague and rarely referred to, The Powers That Be do still appear to have relevance among the denizens of ME (as when Gandalf refers to being #sent back", as he still had tasks to perform). I don't think it was the
travel agency in
Valinor that sent him, know what I mean?
There's always the sense of being watched over, but not being interfered with and that's not necessarily a bad thing.
Tolkien gave the
peoples of his world the ability to make their way in the world and refreshingly enough, you never read of them blaming TPTB for their troubles and yet, there seems to be a certain amount of accountability for deeds done as well.
Basically, if religion is what you're after, you won't find much in LoTR. Try
the Silmarillion if you simply must have a dose of how
Iluvatar people related to him and his fellow gods.