I'm certainly no expert on Islam, but I somehow doubt that he's forbidden from hiring someone who is willing and able to cut women's hair. That would be the more likely recmedy, as opposed to; he'll be compelled by law to personally cut women's hair.
Yeah. OR. . . she could respect the fact that his religious beliefs prevent him from touching her - just as those same beliefs will sometimes cause Muslim women to forgo medical treatments - and she can agree to disagree with those beliefs, and still go to any number of other barbers who will serve her, and she will not have suffered any deprivation whatsoever, because the first barber was not rejecting her person. He was simply not allowed to touch her.