Already happening. Ask the Seven Sisters, the big seven all women colleges in the US. From an 2015 article:
The New York Times published an article about Wellesley College’s dilemma. The women only school admitted men who identified as women, but worried about their Title IX exemption. As a women-only college, they are exempt from Title IX admissions compliance as long as they do not discriminate among women. While administrators tried to untangle their discrimination duties, they watched biological men take leadership positions and win women’s athletic competitions, exactly the sort of male primacy that Title IX was supposed to remedy. The other Seven Sisters colleges faced the same issues.
Full article is here. There are many more examples. Google the Olympic Committee vote on transgender participation for another big story.