And yes, 'she was in the female changing rooms (with her penis out)' or 'they were in the female changing rooms (with their penis out)' is correct...
Well that's the difference. I don't want to see a penis in my changing room. I don't want to be compelled to call a penis a female organ. I don't want to have no option to tell the person to get out. And I don't want laws set in place that make it difficult for me or any other woman to not want to see a naked man when I, or my eight year old daughter, are disrobing.
Plenty of women walk around half naked in changing rooms, at gyms, etc. Do we have to enact laws that say certain women must remain clothed?
It's laughable that you think transwomen won't do this. When, clearly they are. Or people who are not trans saying they're trans. In which case, they are. Because that's all you have to do.
Every predator in the country, whether trans or not, can now dominate women when they are at their most vulnerable.
It really is intellectually dishonest to be unable to describe gender but want to make people accept gender identity, to not be able to tell me what a woman is, but claim lots of people identify as one and that sex isn't determined by biology, but many people's gender doesn't match their biological sex.
(Paraphrasing and credits to Vulvamort).
So don't bang on about what it means to be men and women, when you can't define either. Or how a person identifies as a woman, when you can't define either woman or, identify as. Or that some people's gender doesn't match their sex, when you can't define either of those words.
It's like talking to a five year old who just says 'because'.