Surely nobody would make a case for 1).
No TW needs to sign up for a smear test for example. They don't need to be asked to take a pregnancy test. They will never need checking for ovarian cancer. They may be parents but will never be patients on the postnatal ward. However extreme your views, biology must be /sometimes/ relevant.
So then the question is just about where the boundaries lie. Do you say no to lying with pronouns? Or do you just say no when women are in a particularly vulnerable situation like a rape crisis centre or prison cell? Do you draw lines according to how much dedication an individual gives to the idea that they are the opposite sex e.g. consistency over time, GRC, surgeries? Or is it whatever the person says in the moment? Do you make distinctions between women identifying as men and men identifying as women given that in general women are the more vulnerable group who extra protections are given to? And always what are you going to do with people who identify as one of the other 71 genders if you do want to have anything sorted by gender instead of sex? You'll probably need those third spaces even in the most Option1-leaning society possible.
At any point where you move away from biological sex, you also need to ask yourself whether there's any justification to treating "genders" differently at all. If you're using gender not sex it's clearly not because of biological differences. So that's a challenge to any Option1-leaning answers.
The answer may not be the same in all situations.
For example it makes a lot of sense to have sports Open and Female Only. A woman taking part in men's sports is not unduly advantaged, she's disadvantaged and if she can keep up good for her. A third space doesn't really work though if trans people can muster enough for the odd exhibition match then knock yourselves out. And NB races are clearly just another category for males to win.
But if it helps people to have a few extra, private 3rd spaces in the changing room area then why not, that seems a reasonable accommodation to ask for.