I may upset some people for this thread and, if I do, I apologise before hand. I am beginning to wonder what things are coming as promoting equality has now gone beyond the bounds of reasoning with people seemingly dreaming up all types of things.
Trans gender people seem to be in the spotlight for discussion even to the idea of having different loos for them. There are only two types of gender, male and female and which one that relates to a person is decided by the body organs one was born with. It has always been like that and separate loos are provided suitable for each sex, male and female. One cannot be anything else. I know people have had doubts about their sexuality and many sex changes have taken place. From discussion that takes place now more people seem to have it in their heads they are trans-gender, but the main point I was going to mention is that the equality brigade seem to be peddling the issue and putting ideas into people's heads, especially younger people, that makes them doubt their sexuality. Why ? Peoples body anatomy hasn't changed since the days before humans had developed from monkeys, if true, another issue.
You have already been thoroughly debunked by others, but I would like to say my own thing. Almost every sentence within your post is wrong and offensive.
People, barring those with the previously mentioned genetic conditions, are born into bodies which are one of two sexes - male and female. But gender is an entirely made-up thing. What we see as "male things" - sports, railways, cars, fighting, construction, etc - or "female things" - cooking, horses, fashion, childcare, etc - are societal constructs, based on millennia of men trying to control women. Our society compels people to be one thing or the other - boys play with dump trucks, girls play with Barbies - but people aren't like that. People are a rainbow, we force them into pink and blue.
Further, people may be confused about their sexuality, but that has nothing to do with being trans. Being trans is about your body not matching your view of yourself. We all get that to a degree - maybe you want to be more muscly, or maybe you want to be fatter. Things like that we can change (relatively) easily and without medical intervention. But some things you can't change like that.
That's OK up to a point, which is reached at which others would be reasonably concerned for their own safety by one's presence in the toilets. It is hardly a phobia if there are reasonable grounds to be concerned for one's safety.
Trans people are much more likely to be abused in toilets than cisgender people, and others have pointed that out already. But when you think about it, isn't this a pretty shoddy way to run a society? You don't want to have transwomen use the ladies' because you're worried they will be sexual predators. That's a pretty ****ty way to run a society. First off, it's insulting to sexual predators - it's not like they can't walk into the "wrong" bathroom without having to undergo medical intervention. Secondly, it's insulting to everyone else because you're assuming that all men are sexual predators. This whole fuss over the "wrong" bathroom would be solved if we ditched gender-segregated bathrooms. There's no good reason for them - I'm sure we have all used gender-neutral bathrooms. In our homes they're just called "bathrooms". It's only in public that we have this split between male and female bathrooms, and there's really no need for it. I don't know about you, but when I use the bathroom I go there to excrete, and it doesn't matter if the person in the next stall is male, female, other, or an alien from Betelgeuse VI. Removing gendered bathrooms would also solve the big problems that women have with regards to not having enough bathrooms, given that they generally need to use them more frequently and for longer, yet "equality" is built in with equal numbers of stalls for men and women.
TLDR: OP is offensive, down with the patriarchy, down with gender entirely.