I recently spent some time chatting to a few MPs from different parties.
They all agreed- trans people should have equal rights, and support to transition- whether medical through drugs & surgery, or however the person wished to be.
2 of them were unaware of the self ID possibility, and were very concerned about what this would mean for women. They all agreed that this could be used by predatory men to get access to women only spaces.
So keep writing! For many it has not yet come up as a subject, and they need to know women's concerns.