Just for context, I am pro women’s rights and probably would be classed as holding gender critical beliefs (which is ironic really considering my job).
But what you have posted here is factually inaccurate.
Where a person undergoing gender reassignment is compared to someone who is not, that is covered by direct discrimination in the EqA. But that isn’t the only type of discrimination covered!
GR individuals are also protected from indirect discrimination (which could cover a requirement to use specific sex changing spaces) and harassment or victimisation depending on context (others failing to use their correct pronouns - which would probably only apply in the context of employment, or the provision of goods and services).
But the EqA DOES protect GR in the examples you gave. I say this because I believe that people holding gender critical beliefs are more likely to be taken seriously if they understand fully the law and reasoning behind those beliefs. But putting forward legally and factually incorrect information won’t help the cause and is more likely to damage it.
There is an interesting counter point to this too though after Maya v Forstater which means that gender critical beliefs can potentially be protected in law under the religion/belief discrimination legislation in the EqA - provided that they are not manifestly inappropriate. So ultimately where there is a clash of two protected rights, provided that they aren’t “manifested” in an inappropriate way, there should be some protection there at least.
I would take that to mean that you should use a persons chosen pronouns, as that applies to gender, but expecting to recognise that person as a biological male/female should not be required. But harassing them over it would still be unlawful.
And I suppose theoretically that if you held a genuine and appropriate belief that single sex changing spaces should cover biological sex only, with good reasoning behind it (not just the blanket “but they are menz and I might get raped”) then that could be covered too… although from a public policy perspective I can’t see that right trumping trans rights, as much as I personally disagree with that.