I have sympathy towards JKR whilst also having sympathy towards trans people and I am honestly SO CONFUSED. There are so many elements to this. I'm not even sure what the ideal end result is?
Idea 1. You shouldn't have to transition. Having studied gender identity and gender dysphoria, I both agree that it is extremely real for a lot of trans people to feel like they are in the wrong body whilst also agreeing that this feeling is also a product of our terrible categorical society. I HATE gender stereotypes and sadly, trans people I know have come from extremely sterotypical backgrounds where the opposite gender makes sense to them. If you go into this entire argument, then it generally concludes with the view that very few if any people should be making the full transition. (And those who do are truly unique cases - again if this should ever happen is debatable). This means that boys and girls should be able to dress however they like whilst STAYING boys and girls. Therefore boys can dress like girls with long hair and nails and nail varnish, love babies, be 'sensitive'. Girls can dress like boys with short hair, trousers, have 'masculine traits'. Anyone can do whatever they like but men keep their penis whilst doing all of this and still feel happy to call themselves men. Women keeps their vaginas whilst doing all of this and still feel happy to call themselves women.
However, this then totally contradicts point 2. 😫
Idea 2. A trans woman who has not completely transitioned cannot use a woman's bathroom/safe space
So you must use the bathroom that matches your genitals, no matter how you act and dress. This is assuming that you NEVER transition and it is impossible to be in the wrong body.
So a boy who dresses completely like a girl, but has still has kept his penis (because in point 1 we shouldn't have to change our bodies) still has to use the boys toilet, even though he looks EXACTLY like a woman on the outside.
So in men's toilets people look like men and women.
In women's toilets people look like women and men.
We can't see anyone's genitals so we dont know the truth. Why do we even have two separate toilets?
Oh wait, some men are perverts.
Ok, but aren't the men who look like women also at risk in the men's toilet? Especially if they really do feel like women! Because the magic therapy (if it works) hasn't worked yet?
So are we really just confining people to their genitals after all? 
Then we also have Idea 3. Society sucks. We cannot change it in time. We cannot completely dress and act like the opposite sex whilst staying the same sex so just let people be happy and transition? ohh but how to do this, doesn't work for Idea 2?
Help.
And this is why it's easier to just say TWAW and carry on with your own life.