Good one. Had to look it up as i didn't check for a couple years. Weirdly enough only found one mention within the personal grooming section which is applicable both for cabin and flightdeck crews.
Short beards are generally permitted, but no “three-day stubble”. One has to ensure that shaved beards are always freshly shaved. Dyed beards are not permitted.
Seems to be more about appearance than any safety factor.