Thank you so much everyone. The support is really, really helping. Getting a lot of support on Twitter too and the TRAs have mainly left me alone.
Been in touch with the Equality Human Rights Commission who have given excellent advice and are writing to my centre on my behalf.
Just want to highlight this excellent point from @Artichokeleaves as it sums up everything I am trying to do:
Important to make very clear for the hard of thinking no one here wants trans people to lose services or not have access to services .
What is wanted is female only services available too for females who need them.
For women to have equal access and priority and equal consideration of their particular needs without forced teaming, without requirement to obey and centre male needs or lose services. For there not to be the situation where male people have three groups to choose their best fit from but instead of equality of choice, women get only one whether or not it's a good fit, and female people who cannot use mixed sex provision have no help or services at all.
This centre could have spared the space and staff for one single additional group on top of their offer. That some would struggle to tolerate its existence, even though their own needs are fully and properly met - that's not acceptable behaviour. It's not. It's not ok.