"a large pair of Mahometan whiskers"
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Mahometan or Mohammedan was another word for Muslim, reflecting Islam's veneration of the prophet Mohammad

Devout Muslims are expected to grow their beards as commanded in the Hadith:

The Prophet said, 'Do the opposite of what the pagans do. Keep the beards and cut the moustaches short.'

-  Volume 7, Book 72, Number 780

Interestingly, the Turks on whom Crusoe models his facial hair have turned this edict on its head.

Beards in Islam