Its all to do with partial pressure of O2 required to flash burn the rotten food and other deposits in said facial hair ... I suppose you could say you could have a beard but enforce a degreasing wash of the facial hair before flight.
As a long time beard wearer I am somewhat miffed at the suggestion that my beard contains rotten food and is greasy. I shower every morning (at least) and invariably shampoo my beard and hair (what's left of it). A woman I was talking to once said she didn't like beards as they were "unhygienic". I suggested that if she was like most women she would probably only wash her hair every 3 - 4 days, and so my beard was probably a lot more hygienic than her hair. Didn't go down too well. In any case FAA aircrew on F4s often sported beards and as far as I know they didn't have any problems.