Okay, so this is kind of long, sorry.
Personally, I believe they should, yes. More needs to be done to protect trans and non binary students. They have a hard enough time as teenagers as it is, without making it more uncomfortable for them by forcing them to either out themselves (if they're dressing as their gender but have to go in the toilet of the sex they were born with, for example) or forcing them to not be who they are and express their gender.
I also think uniforms should be a) more comfortable for everyone, b) more 'liberal' and c) have more options for gender neutrality (ie shorts, skirts, trousers, non see through leggings being allowed etc). This is my ideal uniform policy that accommodates all genders, makes people more comfortable, accommodates different budgets and allows high schoolers to be a bit more modern while maintaining a uniform. It's just my take on what the best course of action would be:
Give all genders all of the following options.
Top half: A shirt and tie specific to the school or
A polo shirt specific to the school.
A jumper with the school logo (one colour for the majority, one colour for year 11 or equivalent) or
A blazer with the school logo
Bottom half:Always in black
Black trousers - in chosen fit, but not skin tight for practicality and for protection of all genders from bullying and harassment for appearance, because despite the fact it shouldn't, bullying and harassment does happen and we should be trying to prevent it in all ways we can, as education will not always have an impact.
Black skirt - in chosen fit, but not skin tight for the same reason. .
Black shorts - made with the school logo by the school shop in 2 fits (one more traditionally masculine, one more traditionally feminine - all genders can choose which they want to wear). Must be worn with the logo to prevent too much variation in uniform.
Black jeggings/stretchy trousers/leggings - okay, so hear me out here. some softer, slightly more informal trousers like the average jeggings or treggings, non see through, that are going to be more comfortable and look good with a polo shirt and or jumper.
PE kit:
One kit for all genders here. Student chooses. Either black leggings (non see through, with the logo on) or black tracksuit bottoms (plain), or black shorts in the summer (female identifying pupils may wear a black sports skirt over the shorts if they wish) with a sports polo shirt in the school's colours with the logo on, and a hoodie, either zip up or over the head, with the school logo on the back.
And what harm would it do to have All Gender bathrooms and changing rooms with cubicles *in addition to* the gendered changing rooms and bathrooms?
To all those speaking about the concerns with rape and sexual assault, I understand what you're saying. Aside from educating people with right from wrong surrounding consent, the toilets would have cubicles and no urinals, and the changing rooms would have cubicles (I think not having these is the single biggest downfall of most school changing rooms anyway) to add to privacy. In addition, perhaps a policy where any cis people wishing to use the changing rooms should have to gain parental permission to use them and be monitored (by having reviews of whether or not they should be allowed to continue using them every so often).
Alternatively, and I prefer this idea, you could just let trans people use the bathroom and changing rooms of their gender and provide cubicles in said changing rooms for everyone as well as a communal space, and lockers for people to keep their stuff in (which I am of the opinion should be done anyway). With regards to non binary people, either give them the choice of using the gendered changing rooms they feel best applies to them, or provide them with a third gender neutral changing room they can use with cubicles, and apply the same policy in terms of cis people getting permission to be allowed to use it, and give trans people the choice of whether they would like to use their gendered changing room/bathroom or the gender neutral one.