What Can I Do About Sweat Stains?

Have you tried using hydrogen peroxide in your white wash? It is really good at getting out bodily fluids... Sweat, blood and such.

I think sometimes the problem could be the type of deodorant, together with manmade fabrics, rather than the sweat itself.

Changing to a crystal deodorant might help.  
If they do try one with a holder like a roll-on, and have hairy armpits I suggest using long strokes in one direction past the hairline if you understand what I mean.

Try a natural, organically made deodorant. They don't stain at all.

Rita