"Barbarian" comes from the Greek. It was the word they gave to people who didn't speak Greek, because to them, all of the other languages sounded like nonsense, as if they were just saying "bar bar bar."
And speaking of Greek, it was Alexander the Great who introduced the idea that all soldiers should be clean-shaven, because beard can be used tactically in hand-to-hand combat as something your opponent can grab on to. He was clean-shaven, and ordered all of his generals and men to be clean-shaven, and then it became the fashion. The fashion came and went, as it does, throughout several stages of Greece and Rome, but it doesn't seem to have anything to do with the word 'barbarian.'