You bring up good points but I disagree. In sports its really a non-issue as females simply cannot compete. The chess example is fine, but men again dominate here. There is only one example of a woman winning a game from a reigning male champion. If a woman still wants to play sure.
I am not opposed to this as long as they get equal treatment and no special rules are made for them.
The Citadel allows different physical fitness standards for males and females.
There are advantages to all male education and The Citadel should never have been court ordered to allow females. Nancy is protesting against trans using courts to invade female spaces (rightfully so), however she was fine taking advantage of a court ruling to attend a school that didn't want her there (The Citadel lost a three year legal battle to keep women out). She should be condemned for this.
Fair enough