Sports with incontinence can be difficult. I stress that as I wear more as a back-up, I can't speak for people who totally lack control, but when I occasionally go to the gym I usually wear a pull-up under sports-boxers (you know, those tight ones that channel heat and sweat off the skin. Technical underwear?) with shorts over them. This combo is very discreet and also secure if any leaks happen. Of course it probably doesn't work for heavier protection like briefs and such. Running, I wear the same combo. More secure than guards and, I think, also less visible as there is no risk of the pull-up coming loose. I've heard stories of guards falling from a boxer-leg, although I think that's an exaggeration. There's no way a guard could fall out the groin, especially if one is wearing boxers with snugly fitting legs. Guards, however, may become
loose if one does very hard sports with jumps, kicks or bends, as these put stress on the adhesive strip. Loose guards would be bad for leaks...
I would recommend a pull-up with snug underwear (or, as some have recommended, plastic pants): even thicker pull-ups are quite invisible if held in place by a snug underwear and worn under loose shorts/track-pants.
It's important to keep physically active if possible, and incontinence should not be a reason not to exercise. Of course one has to know their possible limitations and respect their body, but physical health contributes to overall health, of both mind and body, so keep moving, even if you have to risk someone noticing the protection. It's none of their business anyway.
