I think you are over-estimating the power of parents to control how their sons and daughters identify. Families do not exist in isolation, children do not learn to be adults only from their parents.
As soon as a child opens a book, watches something onscreen, seems a selection of toys, is brought to buy clothes etc. etc. they are exposed to the current gender stereotypes. Then they go to school, and unless the school is very careful, and doesn't promote gender ideology, they will get another dose of stereotypes. Then at a shockingly young age, they get a smartphone [as young as 8 isn't unusual] and social media gives them another dose.
The messages the parents have sent to their children about men and women or boys ad girls are just a fraction of the conditioning that children receive about gender stereotypes.
There is no such thing as a child who has been brought up away from any messages about gender except their parents', unless they were brought up on a desert island.
Parents who do their best to instil in their sons and daughters a strong independence about who they want to be, regardless of what society says they should be, often find that either social pressures, or teenage rebellion against everything their parents say, has more influence that parental messages.