In particular when referring to humans, the definition of sex is ambiguous, as is the term “biological male”. And I think this problem is intrinsic: Gender and sex are complicated (with many different markers which may be congruent for many people, but are not for trans and intersex people), and the usefulness of categories depends on context. For example, in a dating context, gender might be a useful category. In a medical context, sex is not a useful category for trans and intersex people: It’s not sufficient information, and sometimes ambiguous.
I agree that it would be nice to have other words than for XY/XX chromosomes (or small vs large gametes), this would make the language more exact and inclusive. However, I (and others) dislike the term “biological male”, because I think it exists only to create a category that equates cis men with trans women. Even if we agree on defining “biological male” as a person having XY chromosomes, in a sports context this is an unhelpful category because there are large differences between XY cis men and XY trans women. When there is apparently so much concern for fairness and safety, why not ask the big questions: How can we make sports inclusive, safe and fun for everyone (including trans people!), regardless of genetics? Are sex or gender useful categories to separate competition — or are there other, more useful markers? (And maybe even: Are international competitions as we have them now a desirable system?)
In the (anarchist) union I‘m in, we have neighborly get-togethers every month, where we talk about our life & work & just eat some food together. But it‘s really nice, there are people of different ages & different professions, so a lot of different perspectives.