How about auto racing? Was Danica Patrick competing with men, not against them? Face it, there’s plenty of sports where women competing against men. Righties are just weirdly obsessed with what’s in your pants (genitals, money etc.).
Being a woman CAN potentially be an advantage in open wheel auto racing. Most, but not all, top tier auto racers are short men who weigh less than average. There isn't a lot of space in an F1 cockpit, and a driver with less mass but equal skill will be faster in the same car, or with equal equipment.
It's my understanding that it isn't as much skill or tradition which keeps women out of competitive racing. They tend to not deal as well with the G Forces associated with the cornering speeds.
There are a number of athletic competitions where women CAN compete with men on an equal basis. In all of these cases, size, speed and strength are not determining factors.
On
Survivor, one of the last few immunity challenges often involves hanging above the ground from a horizontal bar for as long as possible. The 110 pound spinner always defeats the 200 pound muscle jerks in that one.