Oh look another one of these threads trying to apply American theories to the UK population.
In the UK the majority of people believe that sex is real, mammals can't change sex. Gender non-conformity is normal here. Religious extremism is unusual. Unlike America we have strong anti-discrimination law. We are not as homophobic as America.
We are religiously tolerant. We had a very bad time with the Tudors and Cromwell and we decided to avoid telling people what to believe thereafter.
Creationism, anti-abortion, every politician going on about god: those are not things in the UK. Our right wing would be seen as left wing in the US.
You will find that British people will be very tolerant of people cross dressing and/or being gender non-conforming.
You will not find British people to be tolerant of being told they have to pretend to believe humans can change sex.
You will not find the British people to be tolerant of the NHS continuing to offer experimental body modification to troubled children when longer term data became available showing it to be an ineffective and even harmful treatment in the long term. We like evidence based medicine. We like First Do No Harm.
You want to believe women can have the souls of men and vice versa? Go ahead. We are religiously tolerant here. Don't expect me to believe it too. I won't support any attempts to make gendered soul belief more important than biological sex for practical purposes. So fine if a man believes himself to be a woman. Not fine for him to be put in a women's prison or a women's rugby team or a breast-feeding support group.
Your American right wing stuff simply isn't a thing here. Stop trying to make it a thing. We'll just laugh at you.