As a trans person myself I appreciate and agree with the message of your piece, but this phrasing is somewhat problematic. I doubt the woman in question has had genetic testing to determine what chromosomes she has, not that it’s anyone’s business whether she is XX, XY, or has an intersex variant. Charlie was assigned female (as opposed to being “born a woman”) and agrees with that designation, therefore she is a cisgender woman. And as you state, she therefore belongs in women’s restrooms, just as trans women do.