Here is a review of a new book about the origins and functions of religion. I haven't read the book, so I don't know whether its author thinks that explaining religion in naturalistic terms has any bearing on its truth. It does not. To see this, replace "religion" with "science." Science, no less than religion, has origins and functions. Does that mean that science is false? Of course not. Beliefs have both causes and grounds. Science is about the causes (and consequences) of belief. Philosophy is about the grounds of belief.
Another reason why science has nothing to say about the truth of religion is that religious belief has as its object something beyond the natural realm. Science purports to give us knowledge only of the natural realm. By its own terms, therefore, science has nothing to say about (1) whether there is a supernatural realm or (2) what the supernatural realm, if there is one, is like. I honestly don't see the point of these books on the natural history of religion. A belief can be true even if it has a disreputable origin and deleterious consequences, and a belief can be false even if it has a reputable origin and beneficial consequences.
Why are we not seeing books with titles such as The Natural History of Science? If religion can be debunked by explaining it in naturalistic terms, then so can science. For God's sake, am I the only person who sees this?