I understand NC's arguments but, given previous decisions of the ECtHR have set a very low bar for beliefs to be protected, I don't think the courts would agree that GI beliefs are not protected. But let us imagine for a moment that the courts agreed that GI beliefs are not protected. What would that mean?
It would mean that employers could sack an employee simply for holding GI beliefs. They could refuse to employ anyone with GI beliefs, or employ them on worse terms. Shops could refuse to serve anyone with GI beliefs. Service providers could refuse to provide a service to anyone with GI beliefs. And so on. I get that people have been treated like this for having GC beliefs, and a desire for revenge is normal, but that doesn't mean that legalising discrimination against people with GI beliefs is the right way to go. Remember that most people aren't paying much attention to this debate. How many sad face pictures accompanied by "I was sacked for believing TWAW" would be needed to generate public sympathy and allow TRAs to convince people that GC=transphobic?
Yes, some GI beliefs are extreme, but so are the beliefs of some religions. For example, the bible says that male homosexuals should be put to death (Leviticus 20 v13). Some other religions say the same, e.g. Islam. We still protect the beliefs of Jews, Christians, Moslems, etc. However, we don't allow them to express their beliefs in a way that infringes on the rights of homosexuals. We definitely don't allow them to murder homosexuals.
We should certainly ensure that GI beliefs don't prevent free speech or infringe on women's rights, but we don't need to prevent GI being a protected belief for that.
In similar vein, I can understand those on the previous thread who want the WI's actions in admitting trans women to be declared unlawful. I think such a challenge would fail but, if it were to succeed, what would that mean? It would mean that any women's association with 25 or more members could not legally admit trans women into membership even if the (biologically female) membership were unanimously in favour of doing so. It wouldn't just be shutting trans women out of spaces where they weren't wanted. It would be telling women that they can't invite trans women to join their groups even if they want them.
We should certainly point out to WI that the advice they got that said they had to admit trans women was wrong. Since each local WI is an independent organisation, they could leave it up to individual WIs to make their own decision, or they could say that no WI can admit trans women, but they should stop telling WIs that they must admit trans women whether they like it or not. But trying to say that women can't have trans women in their organisation even if they want them is a step too far in my view.