When my sons have gone from long hair (bicep length or longer) to a short conventional man's cut, the barbers never had any issue, though charged them more. They usually paid mid- to high-£20s: much more than a basic barber price, but much less than a basic salon price.
When ds got bored with his dyed hair, the roots were showing and he wanted to return to his regular colour, the barber said that he didn't do colour or stripping out colour, the only way he would return ds to his natural colour was by cutting his hair. Because all he did was cut hair. Fair enough. So that's what he did.
Each time the barbers were asked to deal with stereotypically feminine hair. Situations definitely outside their normal service offer. Yet somehow they had no difficulty recognising that the feminine hair was growing out of a male head, and carrying out their normal service.
As for hair as part of sexual orientation culture being a problem for them - nonsense! Plenty of gay men are particular about their hair and use specific styles as culture messages, and plenty of straight women simply want short, unfussy hair.