Not that I know a LOT of American military personnel, but a couple of guys I went to high school with joined and, well, there's no nice way to put it. They were homophobes. They used to tease the gay guy at our school, and he wasn't even particularly in-your-face about it. (We were a small school, OK. Only one gay guy out.)
On the other hand, I once met a guy through a friend who had just come home from active duty who told me there was a gay guy in his platoon. Everybody knew--nobody cared. There were no complaints so the superiors didn't report him.
I offer these examples to back up Kathryn's closing line. The military--like most organizations--is a mixed bag, much as they love uniformity.
And maybe I'm just a naive, repressed virgin, but like...what's the big deal? My sisters are both very involved in the PRIDE communities in their cities and tell me that their LGBT+ friends are all very big on "Sexual orientation is just that" and it doesn't come with all kinds of other things. (Men loving pink, women riding motorcycles, etc.) So I really don't get WHY it's a big deal in the army context. It's not like there's a pre-ticked "straight" box on the forms. They simply don't care about your sexual orientation--until you go making trouble about it. And if you're making trouble about it, then you ARE a distraction on the front line, just like platoons of mixed male/female straight soldiers.
All that said, I think a dishonourable discharge for being homosexual in the military is WAY out of line. I'm in favour of repeal and institution of a "Don't ask because we don't care" policy.