It's the person that deserves protection, not their belief.
In the past, a man could be sacked if his employer found out he was gay. A gay man deserves employment just as much as anyone else, so that is now illegal.
A person who thinks they are the opposite sex also deserves employment, and cannot be discriminated against purely because they think they are the opposite sex.
The Equality Act doesn't say whether or not the person really has changed sex, it simply says that if they have undergone "gender reassignment" they cannot be sacked for that reason alone.
You've twice avoided answering this question directly, but I'll ask it again. Do you think it should be legal for me to sack a person, simply because I don't like the fact that they say they are trans? If I'm a council housing officer, do you think it should be legal for me to refuse them housing simply because I don't like the fact that they say they are trans?
The Equality Act isn't about a legal fiction. It doesn't say the rest of us have to agree that someone has changed sex, simply that we are not allowed to discriminate against someone purely on those grounds.
A GRC does create a legal fiction, because it says the person should be treated as the other sex - whether for all purposes (including entry to single-sex spaces of the opposite sex) or for some purposes is still to be clarified by the courts.
I used to think the GRA was a good idea for the small number of people who genuinely couldn't stand living as their own sex. I'm now wondering if this is the case, and whether it should be repealed. But I still agree with the Equality Act that no-one should be discriminated against in housing, employment or public services purely because they think they are trans.
I may not like gender ideology, but I don't think people should be discriminated against for thinking they have changed sex.
It deserves no more protection than a belief in fairies.
I could say exactly the same thing about religion. For example, I think belief in the existence of the christian god is no more valid than a belief in fairies. But I should not be able to sack a person simply because they believe in the christian god, even if I don't believe in their god. The Equality Act doesn't make me believe in their god.