The CEO needs to shut up and hire a lawyer.
"All clients regardless of sex, gender, gender identity or sexual orientation are welcome," Carruthers said. "However, we also welcome staff members and respect their religious beliefs and feelings of safety and dignity in regards to the right not to perform waxing services on males or male genitals."
Those two sentences are not reconcilable. Either they "welcome all clients regardless of sex," or they "do not provide waxing services to males."