Could you elaborate? Because I still see this as apples and oranges. Race and gender are vastly different. Race has an amorphous nature where most people are a mix of several different races, while gender is binary with the exception of some extremely rare birth defects. For race to be similar to this scenario, everyone would need to be 100% a single race, with very little deviation. That is not reality.
I find your comparison to race segregation disingenuous at best. You are almost insinuating in a round about way that all that happened with race segregation was we established a black league and a white league for various sports. There wouldn't be so much negative emotion associated with it if that was the only thing that occurred.
Racial segregation involved certain races being completely barred from certain activities. They were not allowed in certain areas, they were denied loans, employment opportunities, education, etc. This isn't about women being denied the right to play sports professionally. It's about whether things would be better or worse if women were competing in the same league as men. Given that even top women athletes would be considered average when compared to top male athletes, I think this would stomp out the possibility of most women being able to compete. This isn't bad for men for the most part, it's bad for women.
Here is an example of the dimorphic nature of our species: "FC Dallas under-15 boys squad beat the U.S. Women's National Team in a scrimmage"