It's extremely difficult to try to disentangle which sex differences (outside the obvious ones having to do with reproduction) are innate, because what used to be called nature and nurture seem to interact in much more complicated ways than previously understood, so that there's now some evidence 'nurture', i.e., environmental effects may sometimes determine which genes get turned off and so on.
The additional reason this is difficult to do is that the it's easy to confuse proximate causes with differences which are regarded as more directly genetic.
Take interest in extramarital sex, the kind with no strings attached, for example.
The traditional view was that it's men who want it more than women do, and in the past surveys even tried to argue that men have it much more than women (even though this is impossible, given that most people are heterosexual and ultimately marry or have permanent partnerships, unless some small number of women have enormous amounts of sex with a vast number of men or unless much of the extramarital sex is gay sex).
But this is probably untrue, and to the extent it is true, it is due to the fact that traditionally sex couldn't be "no strings attached for women" who could get pregnant and who are also much more at physical risk when seeking sex with strangers than men are. Besides, societies tended to punish women for it while men went largely unpunished. Even today men who engage in this kind of sex are seen as players and women as sluts.
Those causes are proximate ones, and should be considered before we simply assume that in their absence women would be less likely to prefer extramarital sex.
Similar problems apply when addressing sex differences in aggression. It could be that men are innately more aggressive in all the different ways, but it could also be that physical expressions of anger don't work as well for women which makes them less used and which may also be why girls in many cultures are trained not to engage in physical fighting (and boys may be encouraged to learn how to physically defend themselves or dominate others). Girls and women can clearly be verbally aggressive.
This problem even partly applies to some of those differences which are seen in many cultures and so might have genetic components, if they are linked to reproductive roles vs. provider roles and the way those have defined women's status (i.e., the environment ('nurture') might be the same in all the different countries/cultures).
As a trivial example, there was a historical slice of time when boys were much more likely to be educated than girls, even if it was only upper-class boys.
We now know that this was not because girls can't learn or are not interested in education or must choose between their wombs and minds etc., but at the time the sex differences would have appeared rather universal and so apparent proof of something innate. This turned out not to be the case.
The argument that all sex differences are innate (or decreed by god) has often been used to justify/explain the subjugation of women, and this makes it important to subject any theories about them to strong scrutiny.
This doesn't mean that such differences wouldn't exist; only that the proof for specific types needs to be very strong and rule out alternative or more nuanced explanations, and should not discount the possibility of multiple reasons working simultaneously.