Are gender traits completely a result of societal expectations?

No. Gender traits in humans are largely determined by biophysical processes. There seems to be a vocal political faction that is trying to convince people in the name of liberty and equality that gender traits are completely learned, and therefore arbitrary. But this claim disagrees with scientific evidence. In general, boys play more with cars and girls play more with dolls not because their parents are perpetuating outdated gender stereotypes, but because their brain is telling them to. This fact does not mean that boys have to play with boy toys, or that boys who play with dolls aren't really boys. It is just a scientific observation about average behavior and its link to fetal development.