I have a very personal relationship with this issue. I am not gay, but I am transgender. I realized it while I was an official in Arizona. The last thing I wanted to do was to attract attention to myself over it, so I sort of hid it. Most of my fellow officials knew and took approaches like during games to address me by my last name (I legally changed my first and middle names in 2014). As much as I wanted to get away with it, I also recognized that doing things like showing up for games while doing things like wearing makeup or nail polish was just a distraction. As an official I felt like I should be "nobody" to most people involved in my games so I made efforts to not stand out (I did make it a point to refuse to cut my hair short at least). I hoped that my schedulers didn't treat me any differently and that I could get games based on merit rather than any nonsense.
Vaguely related, I'm now working with the fire department and haven't really thought any differently. It's obvious that I'm trans since nobody knew me "beforehand" like Arizona hockey officials did, and some of them struggle and still call me "he" or "him" despite knowing me as my name (not a name that can be mistaken for a male or unisex name such as Taylor or Jordan for example). I'm still driven by not wanting to be a distraction and just wanting to do my job. If the local media comes around wanting to create some buzz that my town's fire department is working with me, I'd love nothing more than to tell them to f*** off because it doesn't matter. Long story short, I feel like I can relate to what they're going through.
It's a tough thing though. Ideally, it shouldn't matter. In practice, it still kind of does, but if you act like it doesn't matter, are you part of the problem or part of the solution? I don't know. I just really don't know.