The problem is we established the "gender is fluid" in other context without "but not chromosonal gender" caveat.
I don't think that's an insurmountable problem, though.
What's needed is a clarification of language and concepts. In the past history of testing for sports eligibility, sloppy inaccurate ideas have been promoted: that many sports are or should be segregated by gender, and that genetic testing (karyotyping) reveals ones "true" gender.
The latter notion is false; therefore the former one can't hold. We cut out the "gender" middleperson and say instead that some sports are or should be segregated by karyotype, and that karyotyping reveals ones karyotype. Both are much more defensible claims.