OP's gone, but I'm glad she asked why GRC is a concern when trans women are already appropriating female spaces, resources and our political and social voices without them.
The gender supremacy movement (this being the movement for the supremacy of gender identity over sex) has mutated its concept of gender over time. The pattern has been to gain a legal concession based on one concept of gender, then asset that right for a much wider idea.
So, medically transitioned transsexuals were already living as women. However their actual sex, male, would be revealed by their legal documents. They wanted this concealed for their own privacy so the law gave them a legal fiction to allow them to conceal their birth sex. They didn't need the GRC to live as women, it didn't "change" anything.... except the tiny little detail that it established the concept of a legal sex which can be different to your birth sex.
The next step was to flip this concept 180. Legal sex was established as a legal fiction but the GS movement used it to claim the law recognizes male people can BE women. In GS eyes it's not longer a legal fiction, it's a legal record of fact.
So the concept the activists present of the trans woman mutates from the concept under which the GRA was shaped, ie men who are compelled to live "as" women, wanting to live as passing facsimiles of women and needing a GRC to maintain the il/de/lusion - to men who just are women, and who can be as openly, obviously male as they want because their gender isn't related to their body.
But now, the GRC, established as a legal fiction concealing birth sex to support the "as a women" trans women, becomes a problem because it was based in the assumption that the trans women needs the legal fiction to hide her maleness. In that model, her need for it - her "womanhood" if you will - has to be in some way proved or earned, and that doesn't match the new, was-always-a-woman construction where maleness is fine and a GRC is not a fiction for privacy, but a validation of the fact that she is and always was a woman.
So now the demand is for the law to change again to "catch up" with what trans women are already doing. "It won't make a difference, after all they are already in your spaces, and taking your resources, and replacing over your experiences with their own stories of womanhood"
But what it does do is move that baseline another jump, from a GRC being a legal fiction to preserve the privacy of someone living "as a" woman, to a enshrinement in law that a male person is a woman if that is what (s)he says (s)he is. The concept of womanhood is relocated in the law's eyes from the body to the mind/will, not just for trans women but for all women.
So, the important thing isn't what someone can do the day they get their GRC that they couldn't do the day before. It's what further mutation of the concept of gender will it be used to normalise?