Turns out that actually, yes, they are causing trouble
Is it your understanding that trans people as a group are "causing trouble" in toilets?
and they believe they actually are entitled to be there
So it's your position that trans people are allowed to have a safe and dignified place to piss, but only if they understand their place, which is beneath yours? I don't understand.
and they're actually calling themselves women
Yes, indeed, that's what it is to be a trans woman. Is it completely necessary for you to have such a strong opinion about what someone else calls themselves?
And openly hate women
Is it your belief/ understanding that trans people as a group "hate women"?
This is what I mean by online radicalisation. You sound like someone who had a - perhaps not fully informed - but nonetheless a fairly reasonable, human position on the subject once upon a time.