Who is being backed by the government and all the major political parties? Transwomen are. Lesbians aren't.
I'm getting on a bit now but when I first came out there was an unequal age of consent, I could stil have been legally sacked for being a lesbian I couldn't marry. My relationships weren't legally recognised in any way. I had a spell in hospital and my girlfriend had to pretend to be my mum to get access to my hospital bed. Section 28 was about to come into force.
In the run up to section 28, the media were savage about gay people. They accused us of being perverts, trying to recruit children, having a 'gay lobby', of wanting to abuse children and having 'pretend families', so that we could abuse children, lesbians were presented as being 'unnatural' and I know a few women who lost their kids. We were also, of course, accused of spreading AIDS, while we watched our friends die of it, in a really unpleasant way.
It's loads better for gay people now. However, if you take away the dying of AIDS aspect, I see a lot of those accusations levelled at trans people. The underlying inference is always that trans people aren't safe to be around, that they have nefarious reasons for wanting to use the loo that matches their gender, that they are out to get someone.
I'm indifferent to self ID and I don't mind who pisses where but the narrative being framed around a minority group being dangers, is one that's familiar to me. I remember it being aimed at me and my community and I remember the isolation it caused. I do care about this 'trans lobby' nonsense, I remember it being claime that my fellow gays and I were part of a similar, powerful, lobby, who were trying to take something from the larger community, it was a lie then and it's a lie now.