And we probably agree with you about more than you think. For instance if I met your friend I would be polite (as I am to the various transwomen I know in RL, all of whom are very nice people). I'm always relieved when my trans friends get past the "gatekeeping, must perform my shrink's version of femininity" stage and relax into presenting in a way they seem more comfortable with day-to-day (and which to me comes across as less of a stereotype).
But that doesn't change the fact that I believe certain spaces and activities should be single sex, because there are a small number of circumstances (less than 1% of my daily life) where biological sex matters. My non-negotiable list is women's prisons, women's communal changing rooms, women's rape crisis centres, women's domestic violence and homeless shelters, and women's sport.
The rest of life - meh, knock yourself out. I don't care how you dress, what you call yourself. I want you generic you) to find housing, jobs, live free from harrassment and hte threat of violence, have all the same human rights as the rest of us.
But not women's rights, because when you dig down (reproductive rights, right to free assembly away from the threat of male violence, rights which protect our employment against threats to it due to childbearing) - all specifically women's rights have their roots in biology.