My son had access to everything from beanie babies all the way to cars and trains. Most of the time he liked playing pirates or dinosaurs, but a couple of his beanies were very special to him - he would sleep with one of them, but he typically played with "boy" things....and this is typical of young children. Given the choice, most young boys will pick toys like cars, tractors or other traditionally "boy" playthings, and girls will pick softer toys, dolls and toy kitchens.
Even in infant studies, baby boys are very different than baby girls. So suggesting that there are differences in the genders is not stereotyping them, but simply celebrating our God-given differences.
Social construction happens on top of the natural differences, and there is nothing wrong with this either. If God had not intended there to be differences, he would have created us all the same, and culture would never change. So there are obviously differences as well as similarities. Every culture and every age has varying degrees of differences and similarities.
The Bible fits all people for all time, so while there is equality, there is also "difference" as someone noted earlier. But....we are also not to take it to the other extreme where each person has nothing in common with anyone else alive, just to avoid inaccurate stereotyping. As I said, equality would be a great thing....but there will be a lot of growing pains to reach that point, and both sides (male and female) contribute to both the good and the bad - when you look at society as a whole. Individualism to an extreme, imo, is contrary to God's word....after all, we are categorized by being part of the same faith. And believe me, the stereotype of Christians in the "south" (southern US) is actually very damaging, but they can't see how they contribute to their own persecution and live down to the stereotype.
Any and every social change will hurt some people....there is no avoiding it.