Presumably they'd have to live as a nonbinary person generally, which would come with all the social consequences of being 'out'. Also it may be possible that male-only categories are still rewarded greater than other categories (eg. womens tennis vs mens tennis and other controversies).

If someone wants to cheat, there's easier ways to cheat (doping) than taking on a whole pile of societal judgements in every facet of one's life, constantly, and trying to push against it in affirmation of one's own identity. Including accusations of lying about it for the win.

EDIT: Of course there's no way to objective prove a gender. We don't even have 'objective' ways to prove someone's gender even when they fall upon the binary. We have cis women who have been disqualified for having the wrong chromosomes even though they have qualifying secondary sex characteristics (which athletes have also been recorded needing to be subjected to invasive exposing of their bodies to verify the category).