We're living in a misogynistic world where every single one of us has a sexual assault story (often multiple, many of us from before we were adults), and your priority is 'what if a trans guy turned up at the barbers'. Here's your answer: they get a haircut, because hair is not gendered and cash is cash.
My older sons tend to go to the same barber because the woman there knows my middle son's deaf, and lip-reads to get by. She doesn't chat while cutting, and always moves in front of him to ask questions. Both of them like that she's so normal about this, rather than exaggeratedly mouthing words at him. (People can be very weird about difference, you see - it can make them resentful, defensive and very angry.)
I once asked her to cut my trans son's hair, long before he came out, and she hesitated because she didn't have the qualifications or experience to do all styles. When I said I just wanted his split ends trimmed and fringe cut, she was fine with that.
Barbers can set up with minimal training, while hairdressing (which is more complex styles) requires a lot more education and experience. Do I really need to say that cis men often maintain more complex hairstyles than your average pop-up barber can handle, so go to hairdressers instead? And that cis women wanting a quick trim go to barbers?
Anti-trans activism is popular with cis men because it promotes segregation and allows them to pretend that women are usually safe, with places to go which protect them from harm. That's not true in the slightest, but anti-trans panic is promoting it.
Working-class women work at very close quarters with men all day, share public transport with them, are vulnerable to predatory landlords and are far more likely to be sexually assaulted than more privileged women. 'Meeting someone trans' is not even on our radar as a threat. Diversity is not something most working -class women are unfamiliar with.
For example, I've been intimately examined by cis men in emergency departments many times, usually during pregnancy, when no female doctor was available. I always asked for a female chaperone. And I'd far rather have had a trans female doctor treat me, because trans women understand how vulnerable cis women feel in those moments. I'm an abuse survivor and find such moments incredibly difficult.
'What if' scenarios about trans people are no help to us, because we have actual problems.