Of course, the military ... are filled with religious zealots with a disdain for "those queers"
do you have a cite showing that this true at noticeably higher levels than the general public? 'cause it's not true in my experience, but that's just anecdotal about my little corner of the USAF. If you have facts, I'd be very interested to read them.
You excluded the important part ([its supporters]), but as I believe I've mentioned before, your experience in the Air Force likely isn't representative of the armed services at-large in most demographic terms (those who join USAF I can't see being less educated or less secular than the overall military).
Even if it's an indirect connection of sorts, I feel confident in saying that homophobia is more prevalent in the military than among the general population - and the only modern-day justification for such is religious influence, whether it is direct or not. If there is less religiosity among the military than the public at-large, then it's almost certainly predicated on hordes of poor people being absorbed into the Army/Marines that don't attend church services but nevertheless absorb the more toxic elements of its teachings culturally (and if they do believe in a higher power, I'm frankly unwilling to make a distinction, no matter how "nuanced" their arrival at similar antiquated beliefs may be).