Clean and Green is my nontoxic cleaning bible. Its laundry tips alone have saved at least a half dozen pieces, and the salt sweat removal nugget is my fave. Here's what the book recommends:
Salt-water Soak for Perspiration Stains
1/4 to 1/2 cup salt, enough water to cover the clothes in washing machine.
Soak Clothes in salt water for an hour or two. Wash as usual.
Since I'm nomadic, and not always near a washing machine, when necessary I make a salt paste and apply. It works! It works! I'm no John Laumer, so can't explain how, but the salt seems to neutralize the stain and leaves a fresh scent. The only caveat is that I've used it preventatively when the potential for set-in odor is there but no visible stain yet.
For those of you with unlimited access to washers (or if you're a smarty pants with one like this):
Vinegar Overnight Soak for Perspiration Stains
1/4 cup vinegar, enough water to cover clothes in washing machine.
Add vinegar and water to the washing machine. Agitate to blend. Add clothes, agitate, and let sit overnight. Wash as usual.
"Sustainable = stain-free" could somehow be massaged into a slogan. Couldn't it? Somehow? Grab your own copy of Clean and Green here. ::