From a gender critical perspective the solution is just a little more breaking down of the patriarchy. Transgenderism is often discussed as an exercise of male domination over women spaces. I call that Liberalism of the gaps because I don't buy it and I think its trying to force even more deinstitutionalizing fixes into a shrinking hole to paper over problems that I think were results of the previous round of deinstitutionalizing.
There is a monkey paw to be used, but it doesn't have anything to do with gay marriage or lesbian rights.
One of the effects of the US civil rights movement has been asymmetrical desegregation. To put it in terms of a woke privilege hierarchy, more privileged people are not allowed to create spaces that exclude less privileged people, while less privileged people can create spaces that exclude the more privileged.
A concrete example is that women's-only spaces today are far more permissible than men's-only spaces, compared to the pre-CRA era. There are still some spaces that are men-only, but women decide that a men's space should become desegregated, then it stops being single-sex. The reverse is not true; men's opinions on whether Bryn Mawr should be co-ed are irrelevant, while women's opinions on whether the Citadel should be co-ed became all that mattered.
The problem with this is that this works well for women as long as society considers women to be the more oppressed class. But transwomen are considered more oppressed than cis women, and so their opinions override the opinions of cis women.
And this is the root of the complaint by GC feminists. What GC feminists want is a world where (cis) women get to decide what constitutes a valid same-sex space and what does not. But that's a privilege, and in a world where trans women exist, it doesn't make sense why cis women should have this privilege.
The way solve this is to allow people in general to create exclusive spaces as they see fit. Then cis women can create cis-women-only spaces. But a general rule that people can create exclusive spaces would also mean that men could create single-sex spaces that exclude women. And that's the monkey paw: to be able to have the power to say "no" to trans women, cis women would need to empower men to say "no" to them.