By saying these aren’t real transgenders, you are engaging in the “No true scotsman” fallacy https://en.wikipedia.org/wiki/No_true_Scotsman
And you totally missed the point anyway. It doesn’t matter. Because anyone, at any time can claim to be transgender or simply change their gender under the current DoE guidelines. “The Department of Education says schools cannot require a medical diagnosis or other documentation to prove transgender status”. http://www.usatoday.com/story/news/politics/2016/05/13/what-does-department-of-education-say-about-transgender-bathrooms/84323146/
And what you are calling for isn’t an end to “discrimination”. There was no discrimination before; everyone has the same right to use exactly half the bathrooms or locker rooms in any school. What you are demanding are additional privilege to use the ones you PREFER. And that is the definition of an entitlement, and discriminatory to any real women who simply want to shower without biological men around.
And of course you engage in insults, since you can’t possibly justify any of this nonsense. It’s funny how we are supposed to take sexual harassment seriously — except when trans people are involved?