I would make the rule: has XX chromosomes, and is physiologically female, she can compete with women, otherwise competes with men.
Yes, but … it gets messy. The world “hermaphrodite” is now considered taboo, but such people exist. And there is a long list of very rare genetic abnormalities in which normal sexual differentiation gets all mixed up. When the gender radicals say that even biological sex isn’t binary, this is what they’re talking about — those few, at least, who understand the genetics, as opposed to those exploiting the confusion to press other agendas.
But that would be objective and rational... sort of like Voter ID.