There are some differences between LotR and the Bible (surprisingly,
). Tolkien's work was published, was put into print, and though there have been some small differences with edited, 'new' versions, his work has pretty much been set in stone from the beginning. The Bible has had a different evolution, being translated from many other languages into the form it takes today, so much that was originally there may have been 'lost in translation'. We also have to take into account that even though scribes aimed to be faithful in what they copied, they often worked under a system of patronage and may have been required to excise unpalatable elements, according to their sponsors.
Three of the four gospels apparently are drawn from one source, which I was taught was known as 'Q', John is the exception. But Matthew, Mark and Luke were all written for different audiences. Imagine if LotR had evolved in this way. Though it does beg the question of whether, in future years, the author could be lost, and differing versions (the 10th film version, the 15th cartoon version, the sit-com, the soap, whatever the imagination may conjour up...) may dilute the original.
This is a world which in many cases is more secular, and we see people seriously calling themsleves Jedi Knights or Vampires or reincarnations of Cleopatra, so the idea of Tolkien's work forming the basis of a faith is not entirely off the wall.