Have worn a beard for years now, and i have colleagues who have worn one pretty much all their working life. There was never a restriction from the regulator about it, just a warning that one should take into account slightly elevated O2 usage in case it is needed. But that has been in europe, no idea about regulators elsewhere.
Now, airlines might have some rules what kind of beards are allowed, most that i know do not allow stubble, but that is more an aesthetic thing than anything else.