Sweat stains can certainly damage fabrics, so staining maybe beyond cleaning if damage has occurred. Perspiration contains chloride salts.
To remove the stains, soak the clothes in warm water with an enzyme pre-soak product (Spectra or Fade Away are two popular brands) or rub the soiled area with white vinegar. Wash in the hottest water safe for the fabric. If the stain remains, dampen and sprinkle stain with meat tenderizer. Let stand for about an hour, and launder again.
Always try a small area to test for colorfastness first.