I'm trying to find the free original work online but Spiro did some interesting studies on the Israeli Kibbutz system referenced here (http://www.city-journal.org/html/15_2_boys_girls.html)
Essentially they deliberately tried to raise everyone to be the same, completely free of gender stereotypes. This was quite an intensive process in a closed community made up of people who all shared the same ideals. Parents saw their kids for a few hours a day then they were sent off to be raised communally. Men and women shared domestic and field work and political rule equally.
After a generation they found the women were demanding the right to spend more time with their children, the men had mostly taken control of the government and field work (not by force, but by natural migration) and all sorts of gender differences in play and behavior had cropped up again in the younger generations.
You couldn't have created a better experiment to study the role of nature v nurture on gendered behaviors in humans (literally you could not, getting consent would have been impossible for such a multi-generational study).
So there you go.
If it were simply a case of training many pseudo-progressive (because they're still trying to force kids to adhere to an ideal they came up with) parents would be facing a lot fewer frustrations as their gender-neutral daughters play dress up with their fire trucks and their gender-neutral sons play war with their dolls.
/also . . . who taught the young chimps that they were girls or boys? At some point they must have figured out that they naturally tend to spend more time with one gender group than the other. Does some older chimp explain to them which role they fall in to?