I see no reason to think human sexual dimorphism implies women and men have no common human nature.
That men and women share a common human nature does not mean that the categories of "man" and "woman", are social constructs disconnected from reality: they are not...
The flood of studies showing men and women have differences in preferences does nothing to alter this.
Human nature is a deeper more robust idea that reaches far deeper than which toys, activites, career or vocation men or women prefer on average...
The concept is deeper...
Differing levels of openness, conscientiousness, extraversion, agreeableness and neuroticism in men and women don't show they have different natures.
Human nature is found in the alloy of those characteristics even when the degree to which we each have them is different.
This means we liberals respect the "inherent value" of each person even if each person has differing interests and abilities.
This would not change even if (and I'm not necesaarily granting this) interest or ability was deceminated along the lines of sex or population group.
So whatever population group construction anyone wants to throw out poses no challenge to the liberal, because liberals are concerned with equality of opportunity, not outcome, and we see humans as valuable at the level of the individual not according to their group.
/fin