As far as I know, there is no relationship between pedophiles and transsexuals. And pedophiles can be male or female.
You are using an extremely case to rule out special situations.
If we go down that path, you should never let your daughter or wife out of the house. After all, it’s possible she could be attacked at the mall.
Whether a man entering a girls restroom is transsexual or a pedophile doesn't matter, as long as the pedophile says that they are a transsexual they are both equally protected. There is no other requirement.
Under the human rights statutes being enforced in states such as Illinois, there is absolutely no legal method by which you can remove any man from a woman's restroom, locker room, shower, dressing room, etc. based solely on his being a male, as long as he says the magic words, “Today I'm identifying as a woman”.
There is also the matter of transsexuals who have not anatomically altered themselves. Should they have a legally protected right to nude up in front of women and girls?
You state that this is a “special situation”. I concur, there are not very many transsexuals and if they are discrete, they can get by without causing waves. However, once provided the right to not be discrete, it is no longer a non-issue.