Seems an easy idea, right? Because Sex is a biologically determined thing and Gender is a socially constructed set of expected behaviours and cultural norms. So if that were consistently held to, that would be the solution.
But it’s not consistently held to. A Trans-Gendered (notice it’s no longer transsexual for the above reasons) person could easily be so and change absolutely nothing about themselves or their lives. After all, if I am a biological male (and biology is settled and separate from gender) and I gender-identify as female, that means I identify with an entirely subjective concept that can be anything I want (though my society may have a differing set of wants/expectations), but what happens in practice is that I would identify as female and the subjective view of female gender, while it includes things like length of hair, clothing and makeup, also includes an expectation of biology.
So, you can’t use a “separate but equal” argument where I am regarded as being viewed as socially/subjectively female but biologically/objectively male, because the social expectation for being a female is BEING female, and being excluded by or from any social construct (bathrooms, sports, etc) is not recognizing the reality of my non-biological gender identification.
I hope that makes some sense (or rather, I hope it makes sense that it makes no sense), i’m on my phone and have trouble organizing my thoughts on a small screen which is hard to edit.
