Incorrect, you are making up terms based on no idea what, definitely not law, and especially not UK law which in it's wide body uses terms sex and gender interchangeably. FWS 2025 is first time there is attempt at some weird unity, but that only applies in scope of EqA 2010 (which means access to single sex SERVICES only, nothing else) until some court or legislation says otherwise.
What you are presenting is exactly the view had in late 90's after section 28 was abolished, where sure people can be "trans" but people can also just decide to ignore it and there was no legal protection against harassment that comes out of it. That's what was decided in Goodwin 2002 (and later affirmed in cases since) as not acceptable.
It even notes that while this change of sex may be an inconvenience to some of the population, the balance of right of the minor incontinentie for small segment of population vs inability to exist in dignity for transgender people is not proportionate, and thus decided that this must be protected under article 8. Because that's how you balance competing laws, take what one side gains, see what other maybe looses, and weight them together.
This is for example how we arrived at sometimes having to suffer a walk across long accessibility ramp instead of just 5 tall steps where there is no space to put both in, because for able people it's a minor inconvenience vs inability to participate for people with limited mobility.
So while you can still not believe in transgender people and their ability to change sex, just as you do not have to believe in nutrients or even human rights of any sort, acting on it by, for example, intentionally misgendering transgender people in the uk in public life context can be a hate crime, and unlawful harassment in the workplace and direct discrimination. Context and particulars matter of course and particulars, but if you know someone is transgender, and you intentionally misgender them while knowing well they do not invite it, you are almost certainly breaching the law.
It's almost like law is more complicated than a soundbite.