I don't agree with this. They are certainly socially relevant - important - when they are made so, from children's dress to playing styles to interactional style and so forth, with male children (at least in the United States) facing much more pressure not to behave "like girls" than girls face (at least before puberty) not to behave like boys.
I agree that this pressure does not occur as often or as strongly from one's peers at this age, who as you say can possess some gender blindness, but adults tend to be the ones who socialize and directly pressure kids to behave in gender appropriate ways.
So given that gender is something that is socially defined, that kids are socialized into from infancy, it does not make sense that you would say that kids will be themselves without defining whether they are a boy or girl. How many little kids do you know who
don't define themselves as a boy or a girl? And with the social and performative aspects of gender (which Stumples actually linked to in
this post in Squiddy's topic), where we define our identities in relation to others' reactions to our social performances, I find it hard to buy this notion that children do this.
Even in your example, you seem to be describing whether you recall categorizing your friends on the basis of gender in early childhood, and not whether they were defining themselves in terms of gender.