I used to think the stains are just the deodorant or antitranspirant, but it seems it is something of that that reacts to the detergent. One tip I was given was to rinse the garments in water before washing them (haven't tried that myself), and to soak the shirts in citric acid for 24h (same stuff you use for cleaning your coffee maker etc). I actually tried that last month and that worked. Not totally gone, but very much reduced.