The crescent flying on a dozen national flags is far older than the religion now associated with it. Byzantium was using it centuries before Islam existed.

The star-and-crescent was a civic emblem of Byzantium, later Constantinople, and passed to the Ottomans along with the city in 1453, spreading from there as an imperial mark rather than a religious one. Plenty of Muslim-majority countries have never used it. Symbols get adopted far more often than they get invented.