I have wondered this myself!
I find it curious that
Tolkien actually does describe religion in
Arda in a few
places in detail in his texts.
For example, in
Númenor, they maintain the sacred hill where they offer praise to
Ilúvatar, until
Sauron comes and corrupts this and yet even he doesn't dare desecrate the space.
Additionally, in
The New Shadow, religious cults worshiping the
Dark Lord appear to be at the forefront of the plot, from what we have of it.
It appears to me that in some places, cultural traditions of different societies in Arda bleed into religious function, such as the
Dwarves great secrecy of language and lineage, in some sense comparable to indigenous cultures that exist in the world today.
I think it is clear however, that the
Elves, being the type of beings that they are, would not have religion in the same way
men do. One clear supporting fact to this is the differences in the after-lives of the two
races: men appear to have some sort of relationship with Ilúvatar that is private, some sort of communion or "contract" or something else, which appears to differ from the elves, which are more like angels, in direct contact with the
Valar. I think this theme is actually woven into Tolkien's work in a number of complex ways.
SO, that all being said, it SURE puzzles me why Tolkien touches upon such important themes so briefly.
I think CirdanLinweilin's point is true, that Tolkien believed it would fundamentally undermine his mythology (an act of sub-creation pointing back to
the One Creator) if he were to infuse his Catholic faith into it directly. Perhaps this is really true! I mean, his mythology is so organic and grown from so many different places into what it became, that it would REALLY clash to somehow go back and make it all Catholic. And alternatively, if he were to just "make up" religions for his world, it seems like that could also prevent his work from properly functioning as the sub-creative mythology that he intended it to be, as basically an act of self-expression AND of worship to the One.
Great post!