The concept of being born in the wrong body is pretty close to religious - you have to believe that there is some essence that makes you which is independent of your body and which is somehow paired up with your physical being.
Except that's not true. It isn't possible, or at least no possible mechanism has been identified by which it is feasible.
Are there some people who feel, for whatever reason, that they shouldn't have the body they have? Undoubtedly so and for some of them it causes immense distress which they believe will be alleviated by transition - whether social, hormonal or surgical. Sometimes they find peace through transition but many do not. But the fact that changing how you look, dress, identify makes some people more content does not mean they have the wrong body. It does not mean that they are literally the opposite sex. It doesn't mean that they are a man with a vagina or a woman with a penis.
And those individuals who feel that dysphoria are only a subset of the group which now fall under the very large trans umbrella now. It's considered by many to be transphobic to assume or expect dysphoria.
There is a push here to entirely rewrite law, and language, based on recognition of a semi religious belief. If the demand was that you should be able to access and attend school based on how old you feel rather than your actual age, that would be dismissed immediately. 25 year old adult male wants to play rugby with the under 15s? No, we'd say that was dangeroys wouldn't we?
Yet access to single sex spaces is being demanded on the basis of a very similar premise.