yup, the aluminum basically acts as a mordant for the natural yellowish stain of sweat and its microbial metabolites

best to skip antiperspirant when wearing white shirts. aluminum-free deodorant (there is no such thing as aluminum free antiperspirant, btw) can help mask BO but will not stop sweat. but if you like white shirts that’s probably a decent trade-off.

zinc oxide is a decent deodorant ingredient that doesn’t prevent sweating but does slow down microbes that eat sweat and release odorous compounds

avoid baking soda if you have sensitive skin as it can raise your skin pH to uncomfortable levels. ymmv