Are gender traits completely a result of societal expectations?

Yes. Upper-layer skin cells and the cells in the front surface of the eyes get a significant amount of oxygen directly from the air rather than from the blood. Human bodies have a huge demand for oxygen. As a result, the oxygen that is able to passively diffuse into the body directly from the air is not nearly enough to run the whole body. Fortunately, we have lungs that can actively pull in oxygen and transfer it to the blood, allowing the body to transport oxygen to the cells by using the blood like a fleet of delivery trucks. Most of our cells rely on the blood delivery service. However, the cells in the outer layers or our skin and eyes are in direct contact with the atmosphere and can efficiently get their oxygen right from the air. Let's look at the eyes first.

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 In general, boys play more with cars and girls play more with dolls not because their parents are perpetuating outdated gender stereotypes, but because their brain is telling them to.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.