This bit in the Williams piece annoys me. This is the next battleground for gender-critical feminists, who would like to see the party drop its support for reform, on the basis that any such move allows for more trans people – generally cast by some as predatory men – to access single sex spaces.
How many times does it need to be said? Look at the crime stats. Almost all sexual predators are male. The great majority of violent crime is committed by males. They don't come with a great big P for predator tattooed on the forehead, so for safeguarding purposes we exclude all males from certain spaces and services. There is no evidence at all that males who adopt a trans identity have a female pattern of offending rather than a male one, so they get treated the same as all the other males. Also, to state the blindingly obvious, criminals are dishonest! They tell lies to get an advantage. So self-ID with no checks, no gatekeeping, is wide open to abuse by predators, i.e. criminals.