It is stated (as a theory as far as I am concerned, but sounds true) that
Joseph Rutherford decided that the beard was OUT, based highly on the
fact that C.T. Russell had a beard.
OTWO's above comments sums it up fairly well. Russell had a full beard, and many Bible Students wore one, too. After Russell died, Rutherford forced his way into the number one spot, and he let it be known he didn't like beards. I guess anyone looking like Russell made Rutherford feel uncomfortable, and for good reason. Rutherford was not the person Russell picked for the job. I think Russell knew Rutherford was a snake-in-the-grass that was needed as a lawyer, but nothing more.
I'm sure Rutherford knew this but he used legal means to become the second president of the Bible Students. Seeing others that reminded him of Russell became a demon Rutherford didn't like. That was the start of the No Beard Policy, and it's continued from that long-forgotten demon which bugged Rutherford from the very start.
I can't help wondering if Rutherford wasn't able to grow a full beard. That might have played a part in this, too.