The ISS and currently used spacecraft have toxic stuff (ammonia, propellants) that makes donning gas masks a life-saver in emergency. Beards may interfere with the seal.
Photo: Wikimedia Commons, NASA (Public Domain).
I'm interested in exact pointers to standing NASA/ESA/Roskosmos (and perhaps other spacefaring nations) rules that limit lower facial hair growth and perhaps stipulate which types of beards can and cannot be worn in space (and probably limit the length of mustache).