Materialist, you're right. People will be very angry with any government which passes Self ID. It's hugely unpopular.
When I've been out leafletting for FPFW only once has someone said they didn't agree out of many dozens who took the leaflets over a number of days.
What was striking was the number of people of both sexes (though mostly women) who came back, having read the leaflet, to ask questions. A lot could hardly believe it was true. All were horrified. A very young man talked to us at length. His sister is a lesbian and he's angry about the hassle she gets from males who identify as lesbians. He said it's homophobic
We also chatted with a transsexual with a GRC who supported us. And it's not just my personal experience that suggests the public don't want Self ID. The Times ran a survey and found 97% of readers opposed it.