The Torah and the Transgendered

Dennis Prager writes: …Torah prohibits men from wearing women’s clothing, and women from wearing male garb. For the Torah, the distinction between men and women is fundamental to creating civilization. When the human being is created, the Torah emphasizes: “Male and female He created them.” And that distinction is made manifest in the commandments against men and women wearing the clothing of the opposite sex.
But for most modern Jews, the Torah’s male-female distinction is anachronistic at best and bigoted at worst.
That is, of course, what much of secular society now believes. Therefore, men who feel that they are women — even if they remain fully male anatomically and biologically — are now admitted to all-women’s colleges. And a biological and anatomical male can play on women’s sports teams, thereby depriving a natural woman of a place on the team and giving their team an unfair advantage in almost any sport.
Likewise, a Southern California synagogue has hired as its director of education a biological female rabbi who identifies as male, wears masculine clothing, is referred to as male and insists on being called by her/his given female name. Obviously, the congregation and the rabbi believe that the Torah’s view on gender distinction is irrelevant.
So, then, here is the question: How do Jews who support ending gender distinctions — electing boys as homecoming queens, admitting males who believe themselves to be females into high school girls’ locker rooms and into all-women colleges, allowing anatomical males to play on women’s sports teams, hiring as rabbis females who identify as males and yet insist on being called by a female name — know that they are right?