I'm a lesbian, and the main problems I've encountered are American culture/organizations acting as though everybody has a spouse (when you're homosexual, your dating pool is small enough that if there's nobody around, there's nobody around, but this hits single people in general), assuming that I could move or live anywhere (the suggestion to live in the middle of a rural area to save money was a lot more dicey for us a decade or two ago, and there are still a lot of places I can't/won't travel), and trying to be sure not to out myself on accident during interviews. I had to practice saying I had a boyfriend so I wouldn't slip up. That kind of thing.
That said, I also wasn't visibly gay until last year. I've never run the interview gauntlet as a butch woman, and I imagine that being a butch dyke or an effeminate male adds a new layer of issue.
They never TELL you they're rejecting you because you're gay (or a woman. Or too young. Or disabled). You just get fewer jobs than your peers.