Just because they don't believe trans women are women (or trans men are men) doesn't mean they will oppose measures that make things easier for trans people
You seem to think that GC women need to outnumber the amount of people that spout 'TWAW' for anyone to take us seriously? It doesn't work like that.
Lawsuits will make them think twice. It wouldn't need to be thousands, all it will take is a few.
The woman who was sexually assaulted in women's prison because transgender rapists/sex offenders have been given the ''right'' to access vulnerable women, is taking new legal action for the harm that came to her due to the MoJ's desire to make 'things easier for trans people'. Women being sexually assaulted by trans people in prison has happened more than once. Every single one of those women could sue if they wanted to.
That kind of thing can't be ignored. If there's evidence that women and girls are being harmed, or being negatively impacted eg; avoiding rape crisis centres or women's refuges because they're not single sex, girls not drinking water at school/skipping school altogether when they get their periods so they don't have to share their toilets with males, then there will need to be a rethink and new solutions.
Making someone else's life easier shouldn't mean making the lives of women and girls harder.