The first thing I do with white activewear is hold it up to a window, or failing that, the nearest bright light. If I can see the shape of my hand through the fabric, it's going back on the rail. White shows everything that darker colours hide, thin patches, seams, the lining if there is one, so the fabric itself has to be doing more work than the colour suggests.
White activewear earns its spot in the warmer months, for studio classes, outdoor runs in decent weather, tennis, anything where you're moving in daylight and the brightness actually reads as clean rather than grubby by lunchtime. It photographs well against a gym mirror and it feels less heavy, mentally, than wearing black in the heat. Where it falls apart is anywhere muddy, anywhere you're on your knees, anywhere with grass stains or chalk or fake tan involved, and I'd never wear it for a long sweaty session without a change of clothes after, because white holds onto deodorant marks and sweat patches in a way that no other colour does. It also shows through on a liner day in leggings in a way that catches you out if you're not paying attention, so for anything with a high sweat output or a cycle that's inconvenient, I'd pick a different colour and save the white for lighter sessions.
Getting the fit right matters more in white than in anything else, because a size too small doesn't just feel tight, it goes sheer at the exact moments you don't want it to, across the seat, across the chest on a sports bra. I size up if I'm between sizes rather than down, and I always do a squat and a stretch in the changing room before deciding, because a top that looks fine standing still can gape or go see through the second you bend. After washing, white activewear tends to dull faster than coloured kit does, especially if it goes in with anything else, so I wash it separately and skip the fabric softener, which breaks down the fibres that keep it opaque. Thrown in a gym bag for a few hours it's fine, but left damp and balled up overnight is when it starts to grey at the folds and smell no matter how good the fabric is.
The one mistake I'd avoid is buying white activewear without checking opacity when it's stretched, not just when it's lying flat on a hanger.