I want to go back to that pie meme upthread and say how much it annoys me with its gross oversimplification of a complicated problem.
Now, on one level, I can see what it's getting at - equal pay, for example, isn't a zero sum game - economists have ample evidence to show that more egalitarian societies have higher GDP per head on average, so both women and men do better out of more egalitarian societies.
But not all rights work that way. Sometimes two putative rights are in direct opposition to one another. Take abortion. Either the religious right are correct, and the supposed right to life of the foetus is the most important moral consideration. Or women's rights campaigners are right, and the right of each woman to control over her own body is the most important moral consideration. But there is no way you can make both of them right - either one is or the other, and the two positions are mutually incompatible. When you legislate, you have to make a decision - either you allow abortion, or you do not, but there is no half-way position.
Likewise segregated spaces. If you accept that some spaces, where people are naked and vulnerable, should be segregated for reasons of safety and dignity, then either you believe they should be segregated according to biological sex, or you believe they should be segregated according to self-professed gender. But you cannot have both. Once you legislate to say one group is in the right, the other group have been told their beliefs are wrong. There is no middle ground.
So, no, really, in this case you slice the pie one way, or you slice it the other, but there is no infinitely large amount of pie to go round.