So, ditch gender, but keep the female-specific provisions we currently have until society had evolved to the point we don't need them any more.
And how this would work in practice is to make single sex provision something you can opt out of but not opt into.
So a female person could opt out (on a case by case basis) of the female-only spaces and protections she has a right to use, but she can’t opt into male ones. Vice versa for males.
Clearly that means third spaces for the use of those who opt out, so parallel multi sex provisions become the norm.
Then over time, as we see single sex provisions becoming unused for a particular situation because although both sexes participate everyone is using the third space, it’s a good social signal that that specific need for single sex provisions has gone.
And so, we hopefully evolve to the point very few single sex provisions are needed, not by throwing them out wholesale because an ideology says we shouldn’t need them, but by ensuring the need has gone before we lose the space.
The beauty of the opt-out not in model is
Firstly the whole issue of trans ideology forcing the label cis and an associated gender definition onto everyone else in order to justify their claim to the opposite sex’s provisions goes away, because you can only opt out of your own sex provisions not into some one else’s.
Secondly, we (society) don’t need to work out in advance what needs to stay single sex and what doesn’t. We just make sure the mixed-sex option always exists, keep challenging sexism, sexist structures and stereotypes wherever we find them, and see what evolves.