Do you every find that your deodorant/antiperspirant gum up in the underarms of your shirts, no matter how much you launder?
Yes folks, I have "one weird trick" (tm) for that; make a paste of hydrogen peroxide and baking soda and let it sit on the spot for a few hours. A tiny bit of scrubbing, and voila! The gummy substance has been dissolved. Launder as usual.
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It doesn't seem to damage the dye, but you might want to try it on a tiny hidden corner first.
ETA; Read through commenter Ellen's comments. She was a textile technologist and has some very valuable information.