I don't really know much about the science behind how men and women as populations differ. However, I wonder if it would be possible for society to have a more nuanced approach to these issues:

Encourage men and women as individuals to pursue roles that match their aptitudes and personalities even if they do not line up with their sex.

Provide wisdom or rules of thumb based on how men and women as populations may differ.

However, the problem that I would see with this approach is that humans tend to be lazy in their thinking, so general rules of thumb tend to become absolute rules.