People often used to assume my son was a girl and daughter a son when they were small, which was odd, because she wore his hand-me-downs. Now, she's the active and sporty one and he's the quiet bookworm... but she loves sparkly pretty dresses. He did too when very small, but the world's taught him otherwise, so he wears very traditionally boys clothes now.
I get where this parent is coming from. I just think that we have to raise our kids to be able to fit into the world we all inhabit, and to be as free as possible from having a target on their backs in the school years, especially.
We don't live in a gender free world. If we did, the whole trans thing would not exist, because any sex could express any gender behaviour without literally having to believe they had changed that sex.
And the basis of women's oppression isn't gender. It's sex. Clothes and pronouns don't, sadly, address that at all. If only it were that simple.