Originally posted by: VinylxScratches
Buy dark shirts.
Won't work. The OP would just have white deodorant stains instead.
If soaking them in Oxyclean or similar has no effect, then you're getting new shirts. Wear a tight fitting tee or underarmor type shirt to keep the stains out in the future.
Be careful with the bleach though, each wash with bleach will weaken the fabric until it disintegrates in the wash.