I have a beard and always specifically mention it in my first email for a booking, as dfk is really important to my enjoyment of a meeting. I haven't had any explicit rejections , but of course I don't know if of the ladies who don't reply that is a consideration.
I also put out a fair few RB's and again specify my beard and dfk as well as the type of lady I'm looking for: a few years ago one wg kept making an offer on my RB's and although right up my street in terms of looks, services and age etc she makes a point of stating on her profile that she can't stand facial hair and goes further in saying ' please don't contact me and try to persuade me otherwise as I won't change my mind', so I didn't bother to reply to her.
So after a few weeks of the same, she emailed me and said ' why wan't I interested in her bids as she thought she ticked all the boxes in my requirements', I replied and pointed out the beard references in her profile and she came back and said ' couldn't I shave my beard off to meet her.!
Needless to say it didn't progress any further!