I think you could have used this as a teaching moment to your child that we accept people how they are and for who they want to be, because it has absolutely no impact on our lives but it means they get to live happy ones.
This blanket statement doesn't work in all cases, does it? Treat everybody the same regardless of ethnicity - yes, of course. Do what you can to make life easier, not harder, for people with disabilities - ditto. Respect others' religious choices - well, this is where it starts to get interesting. Do I have to respect a religion that says non-believers should be stoned or that women should always obey their husbands? Sexuality - people who are same-sex attracted are not hurting anybody else by their sexuality, and the vast majority of the UK population now is happy to let them get on with it. But what about people whose sexuality involves fetishes (almost all men) where they get pleasure from doing things in public that affect others, primarily women, without their consent? What about people whose primary sexual attraction is to children or teenagers? I don't care how happy it makes these people to be able to act on their impulses. It is going to make life much worse for their victims, so they should not be accepted.
Men and boys who say they identify as women/girls and therefore should be allowed into spaces and services set aside for women/girls are going to have an adverse impact on those women and girls. If they take up space in a refuge, if they are participating in group therapy at a rape crisis centre, if they join a breastfeeding group, if they use women's loos or join a women's sports team, there will be women and girls self-excluding or finding that they can no longer get access to this limited resource. Given that women and girls have these resources to keep them safe as well as giving them privacy and dignity when vulnerable, and to give them opportunities they wouldn't have in a mixed service, e.g. winning competitions and setting records in sport, how can you possibly say there is no impact on their lives if males start intruding?