When the answer becomes that a public servant team and organisation have been politically captured and therefore can no longer do their job, it's time to close that organisation. They can't respond to FOI requests: they are whole heartedly anti-women and anti-sex based rights, they just can't say so without making it wholly apparent they've abandoned impartiality, abandoned serving the general public as a whole, abandoned serving the interests of any other minority group, and abandoned all national and government policies to be the voice and stealth law-changing unit for a highly niche, extremist political lobby.
A lot of these teams are going to have to be scrapped and something new put in place from the ground up with all newly hired staff and all policies written from scratch, due to their allowing this to happen. It's an appalling failure of government that this has been able to happen at all without being noticed and nipped in the bud.