I am not sure if a yarmulke should be dry-cleaned.
Even the Pope wears a yarmulke!
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The traditional Jewish knit cap is a yarmulke, also known as a kippah.
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The proper way to wear a yarmulke is to wear it on the Sabbath,
Shabbat, or when in Shul. One should wear a yarmulke whenever
everyone else is wearing one.
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Yes, but find a style that won't fall off. You could also wear a
cap or hat instead.