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Now this is a helluva conundrum!
They could, but not at first. After some reforms janissaries could enjoy some more liberties but for a lot of time they were limited to what they could do. The history tab should add that beards were banned at first and then accepted.
That’s just some bias. They are Muslim and Turks so they must have beard. In reality beards are banned for military and for most of civil servants in both in Ottoman era and in Turkish Republic. Maybe during the period of Janissary corruption they may enjoyed beard but after their disposal no beards allowed again.