Talking for myself being from the UK and friends I have here who are also transitioning from a male body to female body, none of us really care about bathroom stuff at all.
Actually we talked about it the other day, with one person bringing up a similar thing saying about a ''transgender only'' bathroom and to be honest that would be much worse for the people who don't want to identify themselves as trans (in other words transitioning people who just identify as male or female, regardless of body).
I have to be totally honest, I think it is a good thing bathrooms are split up and personally I don't think it matters if people think their rights are infringed because of this, it is a bathroom, where you take a pee or a number 2, who really cares so much about that.
Because the trans community is still somewhat the minority I very highly doubt there will be any bathroom changes as they have to take in CIS peoples (who have EQUAL right to give it) opinions on the matter.
Many CIS women would feel uncomfortable sharing the bathroom with a transexual who they just see as a male (through lack of education or whatever) and would feel uncomfortable having their kids share the bathroom with them to.
Same with CIS males, I imagine not many guys would be up for the idea of having FTM, in their mind, girls walking in and out of their bathroom either.
It would just raise to much confusion and in my honest opinion, someone who gets so caught up over the indignity of maybe having to go to a male toilet, well boohoo, thats the way the world is, I don't like sitting down in a dirty Male cubicle but its part of life and we just have to get on with it, there are far more important things to worry about and this bathroom argument sadly seems to be the focus of alot in the community.
Edit: None of this was personally aimed at the OP, just the general bathroom hype people have