The difference between the mean and outliers in particular areas is what causes the strife, I think.
If a woman excells in some typically-male role, the socially conservative culture warriors freak out because "she's left her natural place" and the socially liberal culture warriors immediately call for quotes to ensure that women make up at least 50% of the role-fulfillers.
And vice-versa for typically-female roles.
Everyone fights the idea that society can be designed to accomodate the hierarchical mean, while being tolerant enough to allow for some outliers.