I don't think that conformity is always cultural. In fact, I think it's pretty obvious it isn't. Our evolution as a social species indicates otherwise, though I think some degree of diversity is built into our genes as well. I see evolution on the whole as conforming to the universe's grand movement towards stasis, in that evolution is, for the most part, steadily increasing organization out of steadily increasing chaos (entropy), and within that hypothesis it also makes sense that the species which would dominate would be the one that was self-balancing; hence, we are both conformists and individualists, both as a species and as individuals, constantly at war with ourselves. (This is also one of the main reasons why I think Pink Floyd's The Wall is such a brilliant album--it tackles exactly that struggle within one human being, the fictional character of Pink Floyd.)

Supposing it happened (which itself you know I doubt, but admittedly is realistically possible), then parthenogenetic females would still re-evolve masculine traits and distribute them unequally among the population. Even for asexual or hermaphrodite species, a non-uniform distribution of hawkish vs doveish traits is most advantageous at the population level.

I don't think that's necessarily true, and I'll tell you why. Males tend to have particular traits and females tend to have particular traits which were fairly dichotomous in our precivilized history, but those characteristics are no longer particularly useful and are, in fact, a detriment to the species. For example, male animals tend to be larger and stronger than females so that a) they can physically dominate females and spread their seed and b) they can physically dominate other males to assure they get the female. Those traits are now a detriment because we've evolved to the point where these are not only no necessary, they are in fact morally reprehensible to us. Rape and assault are crimes for a reason. There are other ways to establish dominance, of course, but most of them are also a detriment to the species (wealth accumulation/hoarding, artificial hierarchies [and other examples of false value], etc.) Moreover, males were primarily the hunters and warriors, but now we have a fairly standardized method of food production which makes hunting unnecessary, and that male aggression tends to get channeled now in unhealthy ways.

Thus, on a cost/benefit analysis, these traits are far more detrimental than useful. And if long-term human breeding focuses on females and develops a more stable humanity, as I suspect it will, evolution will in the long run side with the successful. At any rate, it's moot because we're near the point where we can control our own evolution anyway, if we're not their already. For thousands of years of humanity we were in the Age of the Male. We are now transitioning into the Age of the Female, and then eventually (I believe) into the Age of the Sexless, when breeding will be entirely eliminated, all children will be conceived and brought to term in "test tubes" and all sexual characteristics will be eliminated from the species. Of course, I imagine the genetic materials for the original males and females will be stored for a potential crisis, giving us the same advantages as the Volvox algae ⚠️ ↗, which has both sexual and asexual modes depending on their environment, a truly amazing species that has changed very little over millions of years because it doesn't need to.