I've been put in two situations where as a stealth person I sort of had no choice but to go in men's.
The first time, I just wore my t-shirt under my clothes, so that I didn't have to remove my top, and then I changed my bottoms facing the lockers and kept my legs close together so no one would spot my lack of balls.
The second time, I had to shower because we were swimming and I get a bad rash from the water if I don't wash it off after. Fortunately, the showers looked kinda like cubicles...they were open in the front but had a back and sides. I did the same thing - showered facing the walls so all anyone could see was my hairy ass and back.
I was utterly terrified lol, but it ended up being OK. Here's how I see it - play it by ear. Go into the locker room, clothed, and scope it out. If there's a strategy you feel comfortable with, do it. If not, just walk out and decide what you want to do later.
I have also called establishments before asking if they have special accommodations for people with disabilities, who need more privacy...usually, on the phone, they just assume I'm a support worker who will be bringing a disabled person to change and they will tell me what they have available in terms of private stalls. And when I come, I simply state that I called earlier regarding the "special" stalls and they give me the pass code for the room.
Alternatively I've changed in the bathrooms, when they have them, which is gross but it gives me peace of mind. If you are stealth to the people you are working out with that may draw too much attention but I've never had an issue. I usually just make an offhand comment about how I hate locker rooms and standing around with a bunch of naked dudes. I'm kinda fat so they probably assume I feel bad about my size lol.