There does appear to be this push from the left to make society "genderless" as they think it would help with equality, much like race has been made to be seen as being inconsequential.
Of course, the differences in gender are more conspicuous then the differences in race so I don't really see how it can be done. There are people though (such as the women you knew), that believe that men and women are only different due to having different upbringings.
What's interesting, but not surprising, is that research has found very early differences in language, behavior (aggression and rambunctiousness), physicality, and sociality regarding infant babies. On the other hand, there are certain abilities that are equal or semi-equal during certain stages of development; however, these differences may become exacerbated during later stages of development. For example, in terms of physical strength, boys and girls are more similar during middle childhood. Once boys reach puberty during early adolescents, the differences between physical strength between boys and girls become LARGELY different due to the increase of testosterone (obviously).
But, it's also important to realize that biology is not destiny, and that environmental experiences, primarily shaped by caregivers, plays an important role in how biology is manifested. To say otherwise, is equally as foolish as saying that there are no biological differences. I really dislike the extreme opinions on either side (its ALL biology or its ALL society). The research is quite clear that babies are born with certain temperamental styles (biological) and that environmental influences will shape personality development (early temperament -----> adult personality).
Of course, pure physical strength is A LOT less prone to societal influences. The average male is going to be stronger than the average female, independent of societal expectations--I don't understand how people can even debate this obvious biological difference.