I'm guessing the tradition is that a beautician is for women, a barber is for men. And the laws support the tradition. I think it's a stupid tradition and a stupid law, but what can you do.
Who cuts the hair of a butch woman or a femme man?
I remember when salons used to offer "unisex" hairstyles. What happened to that?
I know lots of women who wear very short hairstyles with undercuts and so on (I did for a year. Prior to that, I had chemo and my hair mostly fell out, so my hairstylist gave me a buzz cut). Is that a woman haircut or a man haircut?