I think mixing male and female sport leagues is a bad idea. I'm not opposed to it, in an experimental sort of way, but the deluded kind of feminists who don't think there are physiological differences between men and women will not like the results of said experiment. It would be counterproductive to their goals.
Take WTA, for example. Now I don't like watching women's tennis, but a lot of people say there is more drama in women's tennis than men's and they prefer it. Male tennis is a lot more homogenized with most players adopting similar play styles. If they absorbed female tennis players into the ATP it would be the death of women's tennis. They wouldn't be competitive and you wouldn't see women at any big tournaments. And the gender pay gap would grow much further.
We din't need to pretend that female sports are exactly the same as their male counterparts to find merit in them. They should be appreciated on their own merits.
The only instances where I strongly oppose mixed gender competition is combat sports, because well, it's dangerous.