In this case, the barber's rights trump the lesbian's rights.
The last time I checked, nobody has the right to force a barber to give them a haircut.
The barber can simply hold up a placard which sez:
"I reserve the right to refuse service to anyone."
RE: The barber can simply hold up a placard which sez:
“I reserve the right to refuse service to anyone.”
___________________________
Not in Colorado or New Mexico you can’t.