I think it depends how GII is framed.
Some GI beliefs might pass the test - eg a belief in gendered souls, or that "you" can be born in the wrong body.
But I am yet to be convinced that a belief that a male body is a female body, or male genitals are female genitals would pass. It's one thing to believe that bread and wine are literally turned into flesh and blood by the power of faith, or that everyone has a soul (gendered or not), because there is a spiritual or metaphysical aspect to the explanation. It's not disprovable. But male body=female body is like believing London is in Spain, or Delhi is the capital of Chile. It's a factually incorrect statement.
Also, the belief that gender identity should be prioritised over sex in law and society definitely interferes with the rights of others.
The salient feature of GII is that it has to be performed and affirmed by other people. So it always involves other people's freedom of belief and speech.
The whole pronouns thing is the obvious example of infringing on other people's rights. Underpinning that is the belief that not to believe that someone else has changed sex is actively harming them and preventing them from "existing".
Did I see someone say upthread that some extreme beliefs of Islam do not pass Grainger, although the core beliefs do? I think that could be the case with GII.
I also wonder if it would fall foul of the tests about being cogent/cohesive/important, or a weighty matter. GII is all about the elevated individual and their preferences. There is no moral lesson that it's based on or that it teaches, whether we agree with it or not. That's partly why its imposition on wider society is both ridiculous and offensive.
Just on Forstater - that case was about a workplace environment. The EAT's remarks about "misgendering" etc applied in the context of maintaining good relations between protected groups at work.
Basically I would be very interested to see the question argued in court or some other forum.
Edited for clarity