One last thought experiment, @beautyisthefaceisee, then I'm off to bed.
Let's say we all agree that "female" and "male" are gender identities, and "women" are people with female gender identities and "men" are people with male gender identities.
Let's say that we also agree that we need words for the two biological sexes, and since we don't currently have words for these things, we will say that "flips" are people of the childbearing sex - whether they actually bear children or not - and "flops" are people of the sperm producing sex.
It bears noting that "women" and "men" combined will not add up to 100% of the population, as not everyone has a gender identity, and some people who have gender identities believe they are neither a woman nor a man.
"Flips" and "flops" combined, on the other hand, will add up to 100% of the population, since everyone is one or the other, and nobody is both or neither.
Based on what you've said above, it seems you would support having single sex spaces such as prisons and rape therapy groups, and single sex sports, for, respectively "flips" and "flops". Let's say you also accept that sometimes it will be useful to refer to "flips" and "flops" in a medical context, for example, "flips" may need antenatal care, an abortion or cervical screening, whereas "flops" may be interested in vasectomies or need prostate exams.
Once you've dealt with those things, in what circumstances do you think you will ever need to refer to "women" or "men"? Once biological sex is removed from the equation and these are purely identities, when do you actually need to use these words?