I read Mirage Men based on a recommendation from Enki.
It's a great complement/followup to Poject Beta by Greg Bishop, which I mentioned a while back. As you may recall, Project Beta dealt with the Air Force essentially feeding the delusions of Paul Bennewitz, a scientist and military contractor to the US military who came to believe that there existed a conspiracy which involved aliens and the US government carrying out genetic experiments in a secret base below Dulce (this later formed the core story of the Dulce Base conspiracy theory, which informed future successors such as The X Files).
The book details how elements of US intelligence have not only been involved in the UFO story since the start but, if anything, have been helping to propagate and disseminate the idea that UFOs exist, that the US government has knowledge of alien life and that the US is somehow in partnership with these lifeforms.
Why is a good question. The authors suspect, with good evidence, that there are elements of multiple psychological warfare and deception programs being undertaken by the US military and, for whatever reason, the "UFO story" is one of their go-to covers for whatever they really hope to achieve. Although the religious angle is not dealt with in the book directly, it is also hinted at that UFO contactee cults were promoted in order to understand the dynamics of New Age religious movements (an area that the CIA psywar division in particular had a lot of interest in).
Richard Doty, who was the AFOSI officer who played such a large role in Project Beta also makes more than just a brief appearance.