The Air Force is full of christian nazi-ism. In fact, it's got several pending/on going lawsuits against them over this. The other branches are better in this respect.
As for being openly gay in the military, it seems like it's a matter of location/unit.
Well so far so good here. 10 years of navy service and my possible husband is active, and nobody cares. I have met his chain of command and already am being treated like a regular spouse. So very well!!