If Tolkien were to have placed overt 'emblems of religion' in his works, then he would have to contend with many more problems than just creating a massive fantasy world along with great stories that appear therein. Was the coronation of Aragorn BCE or CE? What religion were the Southrons? Did he portray a particular religion accurately in that there are different versions/sects of Protestantism, Catholicism, Islam, etc?
Would people then see his work as a religious screed - just a cart to carry a religious message and therefore having no value to those not interested in (1) that religion, or (2) any religion? As stated, his intent was not to proselytize - at least overtly - but to entertain. This actually may be a more effective evangelizing method in that more readers are drawn to the works, and those so inclined (or hooked) may read more about Tolkien's life, and also may start looking in to his religious philosophy...
One of the many reasons that I enjoy the Tolkien world is that I can see it as 'history.' If you look at the maps, you can see how we could get to the present day Earth (with some mental gymnastics, of course). Also one assumes that information at the LOTR time was less accurately gathered/archived than when using modern technology. I can fit the 'other history' (some not posting to this site may call it reality
) that I learned in with the Tolkien one as JRRT did not 'timestamp' his by using icons or direct references to real history. It's up to me and my imagination (and culture, I assume) to work out the details...like the Numenorians could have been mistaken for the Phoenicians, and obviously Numenor is Atlantis...
Again, he is leaving the possibility open that what went on in the rest of the world still took place, but in his corner of the world, this is how it was.