The problem is we have conflated gender with biological advantage. If we agree that gender is fluid then we need to stop talking about men's and women's categories. We need to talk about whether of not the racer has the key differentiating physical aspect: testicles.
On ranches there are often 3 categories of related to testicles (Bull/Stallion, Steer/Gelding, Cow/Mare). There are clear physiological difference in terms of size and performance.
So, if we are thinking about adding a new category (as the BA is with non-binary) we don't add non-binary, Instead the race categories become "with testicles", "post testicles", and "no testicles". If you have testicles you have to race in the "with testicles" group. You can identify as male, you can identify as female, you can identify as unicorn but if you have testicles you have to race in that group.
If you have made the choice to remove your testicles/or they have both been removed - for whatever reason, you now race with the post testicles group. In addition, if you want to compete with those with testicles that is allowed. But you can't compete with no testicles unless your testicles were removed before puberty, or you have undergone significant hormone replacement therapy.
Those that have never had testicles only race against each other, but - again - can race against either of the testicle groups if they so choose.
Within each group you can identify as male as female but awards and placement are solely determined by having testes. This by the way also solves the Caster Semenya issue as she is purported to have internal testes and so should race in the "with testicles" group.
You are welcome.