I'm hesitant to say this because I appreciate that one person being worse off doesn't mean another's problems disappear. But when you've had breast cancer relatively young, and seen all your hair fall out, and had to plan on how to make that less stressful for your small kids (kids who, by diagnosis, find change incredibly hard at the best of times) by taking them to the hairdresser with you, and getting them to snip it to a bob with her, so they felt relaxed around the idea Mum was losing her long hair. And when the day arrived when it came loose at the roots and began to fall in chunks, you set them a contest to see who could grab most fastest, and woohoo look isn't Mum's losing her hair cooool! And then you ignore the baldness, and wear hats, and just get on with it, because what's the point in focusing on what can't be changed? Life is short and wasting it on navel gazing pointless and wasteful.
When you've had that experience, people saying that trying to get a hairdresser to understand that they want an unconventional cut (and no cut is these days, anyway - just look around you, in any city with youngish people in it) is hard, is a tad difficult to swallow.
Choice is important. They should be able to choose how they present to the world. And they can. Chemo took that from me, and that was really hard. Not disliking being bald (I actually look a lot better with a really short crop, when it grew back in) but the lack of agency. I grew mine back despite knowing it looked better short, because I wanted to be who decided that. Not cancer.
Gender isn't a concrete straitjacket. Present as you like. But nobody is out to get you. It should not be such a big deal. I do think creating drama over having to ask for a cut that you feel is gender neutral (and what is a men's or women's cut, anyway, really?) falls squarely under the heading of buying problems, when life will hand you a plethora of 'em for free.