I've seen a LOT of posts, over the years, about people expressing concerns about wearing their CB and doing exercise. Some guys insist that they need to be out of the CB for it. That hasn't been my experience.
I frequent four different workout facilities. Three of them have at least one private shower stall. My preferred workout attire includes a pair of cycling shorts beneath a looser pair of gym shorts. It's generally a simple matter to isolate myself in the locker room enough to change out of my normal clothes into my workout clothes undetected. I choose lockers near a corner. On particularly bad days, I've simply taken my cycling shorts into a bathroom stall, and changed in there, No one ever noticed.
Cycling shorts are very padded in the crotch, so they hide the CB very well. I'm completely relaxed wearing only cycling shorts while in the locker room. So, after my workout, I strip down to the cycling shorts, and wear them to the shower, carrying my toiletries, towel, and my underwear. In the private stall, I shower, and dress in my underwear before returning to my locker.
I wear briefs, but not super-tight ones, so again, they obscure the CB pretty well. While walking around in my briefs, I just carry my towel or toiletry bag somewhat in front of me, further obscuring the view of my crotch.
As for workouts, I've done pretty much everything. Running, elliptical, cycling, kickboxing, and aerobics classes. Cycling is the only "iffy" activity. I find that if I set my saddle a little low, it keeps the pressure and chaffing off my balls. It also helps my arthritic knees.
The result has been many years of workouts, 2-5 per week, with no one detecting the CB. It's really not a big deal.