Why would they need to refine stereotypes if there were none?
Children and adults hold the same sets of stereotypes; they are harmful to adults. Unless you think they get rid of them and then pick them up again??
Stereotypes are just patterns that hold much of the time. They may be harmful in some cases, but plenty of them are not. Adults and children see similar patterns because they are observing the same society. Adults and children don't generally hold them in the same way though, as children tend to see them as concrete rules whereas adults generally understand they are patterns but they don't always hold.
But the point of the research on children is that it's developmental, not socially driven - they will develop stereotypical views so long as there are any patterns of difference they can discern between men and women. And they will overgeneralise them, and make them far too concrete.
This is how kids at that age learn about a lot of distinctions, you can see the same thing when they try and distinguish between different types of animals for example, or vehicles. Gross, clumsy generalisations, and that is the raw material that allows them to begin to see finer distinctions, how the rules are broken, which rules have more force. It's almost a kind of testing that goes on over years, sorting and refining the algorithm. But without the initial gross categorisation there is no starting place.
I don't think it would really be possible to have a society without cultural patterns around sex, but if it were, kids would still overgeneralise the sex characteristics they could see in people's bodies, and would need to refine their paradigms over time and as they became more able to see and understand nuances.