I think Dear Keir is arguing that
CAT A) Woman the gender - anyone can have a crack at it
CAT B) Woman the chromosomal sex - XX humans, that lot that don't have a penis
Keir's happy to allow XYs to obtain legally altered paperwork to enter CAT A, because that's nice isn't it?
The two categories then are lumped together in Keir's political philosophy as an exciting new 'gender class' (or he may sometimes pretend it's still a 'sex class' with 'all women' in it, depending on the interviewer and how badly it's going); and Mary Wollstonecraft, Harriet Taylor Mill, Emmeline Pankhurst and Barbara Castle can all go fuck themselves.
I think I've understood the Labour Party's position here.