For me, I think a self-ID system with limitations would be best. I support people's right to express themselves however they want to and people should not be discriminated for presenting in a gender non-conforming way. If people felt having some formal recognition of this gave them extra protection, then having a way of IDing as a transwoman or a transman without too much bureaucracy could be a good thing.
I think people who feel trans and are over 18 should have access to NHS treatment, including hormones and surgery if they want them- as well as counseling services if they want those. I do think that surgery should not be provided completely on demand as it is a major procedure and might not be appropriate for some people. I do not think children should be able to access any form of drug treatment or surgery, but should be given counseling and support.
In statistics, I think trans people should be counted separately from others, especially when it comes to crime, and saying things like "we have x women in senior positions".
I do not think trans people should be allowed to participate in competitive sports where there is a safety or fairness issue. If there was enough demand, trans only events could be organised.
When it comes to prisons and shelters, if possible third spaces should be created for trans people. Transwomen should not be allowed to enter women only spaces in these cases.
With changing rooms, I think we have to move away from communal changing. It causes problems other than for trans people as well, and is basically used as a space saver for a lot of health clubs, gyms etc. I think it should be a requirement to provide cubicles, non-communal showers and family changing spaces that are not communal, and hopefully this would provide a suitable option for trans people.
With toilets, I think more unisex options should be provided- with floor to ceiling doors etc. However, single sex options should also be provided for those who's beliefs mean they do not want to share facilities.
Women should be allowed to retain spaces for discussing issues that only affect XX people with only other XX people.
For young people on overnight trips, there shouldn't be any sharing of sleeping spaces between people who might get each other pregnant- regardless of the gender they express themselves as. Trans students should be offered an appropriate third space/safe space to sleep. If changing for PE has to be communal then trans students should be offered a third space to change. Students should be allowed to wear whatever uniform items they prefer- everyone should be allowed to wear dresses/skirts if they are part of the uniform. If a student wants to wear a dress or tux to prom, that should be their choice, regardless of their sex. If sport is sex segregated in the school, I can see the arguments for trans students to be allowed to take part in non-contact sport with their chosen gender.
I can see that a lot of this is a bit exclusionary of trans people- I've said a lot about third spaces etc. However, I think we have to acknowledge that a transwoman is not a woman, and a transman is not a man. It is important for them to have a space where they can change and go to the toilet and feel safe. However, this cannot be at the expense of everyone else. I do accept this puts a lot of onus on businesses to make new spaces etc. However, I do think this is the best solution.
I also think it's good for young people to be able to experiment with gender expression without having to put a label on it.