Good question, Linda.
I wonder: is there any reason we aren't moving more towards un-gendered competition? Ellen had an interesting point about
women ultramarathoners who have been doing spectacularly well in mixed races. Just to throw some ideas out there... maybe somebody wants to open up a major sports event to everybody who cares to enter. Or to group people by height and weight like in wrestling, rather than gender.
I don't actually know how different male and female performance is, or what sports would be a good place to start. Obviously world's strongest man is going to stay gendered; distance running might be a fair contest; probably horseback riding is no problem. Surely with other sports people could come up with clever ways of mixing up the terrain or the task so that both genders would have the advantage (a triathlon requiring both upper- and lower-body strength, or sprinting and endurance, aggression and cooperation...that was a joke).
Anyone want to propose a 21st-century triathlon which would make a good, fair contest? -- where "fair" is judged by, say, betting odds on winners across genders.