Well, since "gender" as used by the turn-of-the-twenty-first-century Left is a characteristic determined by the subjective feelings of the person in question, speaking within his own frame of reference, he is right. Sex, however, is easily determined from any reasonably complete set of skeletal remains by any competent archeologist or forensic pathologist (or even from a little bit of bone marrow if genetic tests can be applied).
The mischief we are enduring in this regard is caused by the demand from the Left that we replace the objective biological category of sex with the subjective and socially constructed category of gender as a matter of law and in all social discourse. Doing so is manifestly harmful to women in sport, to women who are incarcerated after conviction for a crime, and to women seeking shelter from domestic abuse, and somewhere between actually harmful and merely annoying to women who use public toilet facilities. (Here I use the English word "women" as it has been used by all English speakers since the pronunciation shifted from the Old English wifman until the last five minutes, world historically speaking, to refer to adult female human beings.)