We've known roughly this since The Nurture Assumption (1998). Where parents do have an impact is in being able to choose the social circles their children are immersed in.
The discussion of toddlers more or less code switching is quite interesting.
Once they have a sense of self, even little kids will be very careful about revealing their home life to their school friends, and the same about school to their parents.
Haha I can see myself in that. I was terrified of my mom knowing what my school social life was like as I felt terribly embarrassed that some kids made fun of me and things like that.
