It only applies to the minors. It's the same as the drug policy differences between ML and the minors. It's because at that level, the younger men don't necessarily know how to behave professionally yet so they have to institute rules to ensure a certain maturity.  See: Shelby Miller. 

Now you may say what do beards have to do with baseball?  No harm, no foul right?  Right, but young men with patchy beards don't look professional. At that age I thought my facial hair was awesome but looking back, I looked like a bum. And it's easier to set high expectations early on so they carry over to pro ball. 

I do agree it's still outdated policy though.