This situation is very yanivy.
If there's even truth to the story. I've never met a hairdresser who outright says that they won't do a specific cut on a person, especially so if that person isn't even present. I have seen conversations where they advise against a haircut once seeing the person because they feel it isn't the right cut or they'll offer up options they feel would be better suited, but I find it very hard to believe that a hairdresser would outright refuse to do a haircut based on the voice and request of a person on the phone. They're offering a service, they don't get to make decisions based on their own wants for a customer. Short hair on women in this day and age is pretty common, wanting a 'male hairstyle' is not asking them to cut off your fingers or something. Heck she could have easily said 'female haircut' when on the phone and brought a photo of a woman with a 'male haircut' when she went in person it ain't that hard.
How would a salon even know the haircut is even for the person booking? Heck, most hairdressers I know book based on the service to be rendered- wash, cut, trim, cut and color, eyebrow wax, etc. Sure male and female haircuts can have different pricing but the question should probably be more about the length you're choosing. Are you going long to short, short to shorter, etc.
I have heard of barber shops that usually turn down female clients and I get that in the sense that if they can book for both hair and beard care, where they make more money, vs. a woman who just wants a haircut - they're obviously going to want to book the client that gleans them more revenue.
I always feel like when it comes to 'haircut' stories they aren't fully explaining the story or there was some misunderstanding.