Years ago, when I was a lowly MS, an elder showed me a letter a brother in the congregation wrote to the branch asking for an explanation about why brothers could not wear beards. The branch responded. It basically said that a brother could wear a beard if he so desired, but could not have any privilege in the congregation, nor give public prayers. The only exception was if a beard was covering an embarrassing facial blemish (e.g. deformity, rash, etc.)
I knew one elder who had a beard because of a facial blemish.
I knew another elder who got removed because he grew the tiniest bit of hair below his bottom lip and refused to shave it off. He was deemed "proud" and "haughty" because he wouldn't accept counsel based on man-made rules. He was a real nice guy. I think he faded soon thereafter due to the way he was treated.
Oh, and if you want to see how much beards are frowned upon, take a look at the illustration on page 13 of the Good News From God brochure to see the progression of a resurrected man. Better yet, here it is. Of course, the relevant question to ask is: If God resurrected him WITH a beard, why does he have to shave it later???