I am not interested in a fight. I would like to feel I had been listened to and considered by transgender people, given I am a woman and all, and it is my loos and my locker room and my changing room I may shortly be sharing with people who have penises. I am well able to accept that there are transgender people. That is very clearly a fact. Where I stop accepting is the point where they say they have a right to be in a women's space where women are naked, showering, changing clothes, from age 8 up. I am never going to accept that.
Safe spaces for transwomen would be great if transwomen would accept them, but in the US they do not, and offering a trans space is dismissed as discrimination. They demand the right to use the women's spaces, with the women and the girls.
No one should be trying to prove ones need is more legitimate or greater than another. That has already happened in several court cases in the US. The 'needs' of transwomen were held to trump everyone else's when it came to high school facilities.
Women's spaces are perfectly fine, for women, and men's spaces are perfectly fine, for men. They have nothing to do with gender but with sex, or undeniable biology if you will. Speech that refers to biology is held to be discriminatory, however.
Men need to accept other men who have penises and who wear dresses or skirts or tights or leggings, bras, high heels, nail polish, whatever. The very strongly gendered male world, where there is little room for men who deviate the slightest bit from stereotype is the problem here.
It is not the persistence of the binary per se that causes problems. It is the refusal of men to acknowledge that 'feminine' is equal with, not 'less than' masculine, and equally deserving of respect and acceptance. It is also down to the refusal of men to acknowledge the feminine element in themselves and the right of men not to conform to the stereotype. It is men who force the choice between 'men' and 'not men' and men, (including transwomen) hold the perception that if you don't feel like you fit in as a man with men, then you must be a woman, and you belong with them. This notion is profoundly disrespectful to women.
I agree with VestalVirgin wrt the DD of the OP here -- just because medication, hormones, surgery are available doesn't mean they are for everyone. Unhappiness with your current physical state doesn't mean you should be someone else. Getting to the real cause of the unhappiness is a better option than taking the surface level issue so seriously that someone considers medication, hormones, etc.
I agree with Icanteven, that the internet, posting selfies, living your life in public, seeking (and sadly all to often getting) the attention and approbation of complete strangers and others in your own little echo chamber alike contributes hugely to the current 'trans' phenomenon. I agree with the OP that what her DD seems to be doing is attention seeking, and choosing a group to identify with in order to experience anticipated rejection may also come into it.