There is no such thing as transgender (well there is but I'll clear that up in a sec and it is a very rare genetic condition).
Lets take Bruce Jenner. A man, a father who decides we wants to dress like a woman. A transvestite. At this point, not a transsexual. He then goes and has his nuts cut off. That's a eunuch. A castrated man in a dress. He then has some plastic surgery. That's Michael Jackson. He pumps himself full of hormones, that's a drug addict. None of these things change his sex in the slightest.
Every single cell in his body has an xy chromosome. It is male. He is male. Every brain cell, nerve, tissue all male. He is 100% male, albeit he has mutilated himself.
Now there are transsexuals. It is rare. Women have xx. Men have xy. Some unfortunate sods get xxy. If you get that, I think you should be able to pick which changing room you would like (you end up being very androgynous anyway). Anything else is just someone pretending to be something they are not. I can't enter the 3:15pm at Cheltenam with a jockey on my back because I'm not a horse. I can complain its my dream. I can say I feel like a horse and identify as a horse. I can have surgery to alter my ears and have fur implants and cosmetic dentistry to make me look more like a horse. I can eat winniepro and take horse hormones, I can crawl on all fours, sleep in a stable and wear a bridle. But I'm still not a horse, my dna will be human.
Transgender is bullshit, and anyone with xy chromosomes in a woman's changing room should be imprisoned for gross indecency.