Perspiration stains are a complex mixture of body oils and dirt. Seventh Generation laundry detergent removes them about as well as Tide®. However, complete removal is a function of many factors including the nature of the fabric, the individual's body chemistry, associated soils (including the deodorant used), water conditions, etc. Deodorants should not stain.
Seventh Generation laundry products should do an effective job under most circumstances. If you have a concern, it is recommended and safe to run a little liquid detergent on the stain in question, and let it sit for a short while prior to washing the garment.