Idea: sports competitions shouldn't constantly be chasing the outliers — fastest, furthest, strongest, etc. Instead, the goal should be to hit the mean average in your class. "Closed bids", each competitor doing their run (etc) solo, without knowing the others' times. Most average wins.

*That* should suit your bimodal distribution.

This is surely a winner. I expect the competitive sports community soon to be queueing up to praise me for this ingenious idea.

Elite sports people: "We're here to celebrate extraordinary people!"

Trans / non-binary / intersex / etc people: Cool, let's go :-D

Sports people: "No. You need to be more ... ordinary."