The Muslim woman does not perform waxing on men, that is the agreement that she has with her employer. If she was a white woman, and made the same agreement, then it would be the same exact situation. The religious part doesn't make a difference at all. What matters is that her job is not supposed to include waxing men.
Well first, the fact that she is Muslim is not the point. The point is that she does not want to wax men, and her employer agreed to that when he hired her. No different than going to a salon where most of them will not cut men's hair, but have a barber there sometimes who does. If the barber is not present, you're not getting a hair cut. There are women-only gyms near my house too. It's really not exclusively a religious issue.
I do not think any employer would hire an employee under the agreement that they would not serve a specific race. That is just discrimination and practically begging for lawsuits. Using race as a reason to deny someone service is no more sensible than using their hair color, eye color, height, etc.
I do not put race and gender in the same category in this regard at all. Imagine Mike Pence saying he will not be alone with a Hispanic. Different right?