I was a member of several gyms in my 20's. The gym was nearly always slotted between jobs, classes, and going out. There was rarely any opportunity to go home and most of the time I had to be clean and presentable wherever I went after the gym. Skipping a shower was simply not an option. I'd arrive in one set of clothes, work out, shower, shave, and leave wearing a clean set of street clothes.
Going home and showering would've meant giving up some combination of sleep, studying, income, or time with friends. I can't imagine that's changed. Then again, maybe the guys in a situation like I had are the ones taking the showers.
Locker rooms aside, if I'd had an issue changing clothes in front of my friends there'd have been major problems going to the beach, going to swimming pools, cleaning up from whatever to go out, etc.
I also wonder to what extent this excessive modesty affects their dating/sex life. Last I checked sex worked a lot better without clothes...... Or am I missing something?