The physical and mental differences between men and women are glaringly obvious, and anyone who denies them is merely being pious.
Obviously, I am speaking about political equality
But in an anarchic society you do not really have politics, or at least should not have politics, hence no politics to be equal before. The differences between men and women are such that men will do most of the enforcement and provide most of the protection, while women will do most of the housework. This will have consequences significantly different from a society where the state does the protection, most of the childminding and much of the economic support of women with children.
Now here is something I would really like to know. What mental differences between men and women do you believe are "glaringly obvious"? This should be amusing.
Famously, or infamously, women cannot read the map, and men cannot find the butter.
Men are markedly braver than women, so much so that "pussy" means cowardly, and "man up" means "be brave" Almost all men are braver than almost all women.
Upper body strength: Any man whose upper body strength is no more than that of a strong woman is seriously ill. There is zero overlap between healthy men and healthy women in upper body strength. Some female athletes look like they are counterexamples to this, but those athletes look they are taking male steroids.
Most women are worse at judging position and motion than most men, thus almost all women perceive almost all men's driving as scary, and almost all men perceive almost all women's driving as incompetent.
Because of differences in ability to judge time, motion, and position, a woman, after backseat driving her husband all day, will take a painfully long time parking the car.
While her husband drives, a woman will frequently tell her husband "watch out for that thing", when there is no possibility that that thing will intersect with the car the husband is driving if the car and the thing continue on their respective courses. When the wife drives, the husband will never do this.
Women talk a lot more than men, and are better at it. We automatically apply higher standards to women speaking than men speaking. If a woman speaks no better than a man, we think she is mighty stupid.
Women are better at human relationships in a small number, close and intimate relationships. Men are better at people in a large number of distant relationships. Men are better than women in negotiating hierarchies, at acting within a hierarchy, within a team or large group. Thus men are better at team sports, and enjoy them more than women.
Men are better at logic than women, which creates problems with efforts to affirmative action a sufficient number of women in science and such like. A male computer science graduate can always parse a boolean expression, because he could not graduate if he could not. A female computer science graduate usually cannot parse a boolean expression, indicating that if they required them to do that sort of stuff there would be very few female computer science graduates.
Similarly the fact that we are taught about so much about female scientists who are made famous for strikingly unimpressive accomplishments demonstrates that women just cannot do science very well. If women could do science, those promoting women in science would have more impressive poster girls.