That's one of many ways sex is defined and it's definitely useful for some purposes, but I have no idea why some people think that is appropriate for making social distinctions.
> Women have a right to sex-specific sports
Gender (social, including legal, categories based on sex traits are gender, not sex) categories in sports were almost without exception created to prevent men from having to compete with and potentially lose to women. There is certainly an existing practice of gender segregated competition in some some sports and other competitive domains, but I’m not sure where the idea that this practice of segregation is a matter of rights comes from, no matter what basis of assigning gender is used. (Gender segregation has been frequently used as a means of preserving unequal treatment while meeting the US legal obligation for numerically equal opportunities in school sports insuring, but that’s obviously not the same thing as gender segregation being a right.)