Far east: Rav Moshe has a Tshuvah about wearing a Kippah when going to (either a bar, a dance club, or a movie theater, I don’t remember, but some place you shouldn’t be) because of Chillul Hashem. He says why add a second improper thing onto the first. And yes, I can see that you might be able to be Mechalek here but the basic principle should still apply.
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