There is probably a fairly reasonable explanation for this lady's comments, but that doesn't excuse them. Learning that you don't need to share every dumb thought that comes to your mind is the most outward expression of maturity.
My guess is that when she was younger, she experienced some sort of negative situation that could have been as extreme as abuse by a bearded male relative, or as tame as a bearded teacher giving her a bad grade. For some reason she has a bias against beards and is unable to see that trends are shifting and beards are no longer seen as unhygienic. Why she thinks it is her place to force her opinions on you when it is obvious your beard is not an accident, shows her maturity.
For the record, I agree with your assessment that it makes you look "professorial." It most definitely commands respect, and it makes you confident (at least it seems that way to me). Don't worry about the haters...