Splitting society into two different halves with different traits and responsibilities expected of them based on this one parameter is extraordinarily arbitrary.
Man, you hear this "abitrary" line so often that you'd think people would have examined it by now and seen its obvious flaws. I suppose it's because you mainly hear it from humanities or sociology types who wouldn't know a zygote from a spandrel.
There's a reason why there are differences between the sexes in most of the animal kingdom that has sexes and are k-selected, including humans: it's differential parental investment. In the case of humans, females invest far, far more in an individual offspring than males do.
At the minimum, males contribute some jizz which they have unlimited amounts of. Females contribute an egg (which they have limited amounts of, not to mention a lifetime biotic potential of 30 or so at the absolute max for an ordinary woman), the environment for the fetus to develop, all the nutrition and energy for the developing fetus, the lost opportunities to have offspring with better men for the whole period of pregnancy and often the period of nursing...need I go on? For a male, creating a child is a tiny and near effortless investment. He loses nothing by it if the female or others cannot obligate him to stay with her and help raise it. The female makes a HUGE investment and it nearly always pays her, in darwinian terms, to keep investing in the offspring.
This fundamental fact of reproduction is the reason why differences between gender roles are not arbitrary. This fact leads to evolution of different behaviors and desires in males and females. It's not just due to social conditioning that men are often willing to have sex with a woman they just met while women are far more conservative. It's not just due to social conditioning that deadbeat dads are far more common than deadbeat moms. or that men desire more sexual partners while women would rather have one devoted mate. And on and on and on.
In any case, I'm not sure what this imaginary "unigender" society would look like anyway. I just know that by any reasonable definition of gender, it won't happen. If you're saying you expect that men and women would think the same way about sex and offspring and mating and relationships, well, that unigender society would also have unicorns and wizards.
In any case, biological sex can be a messy business as people are discussing in relation to chromosomal or hormonal disorders (hell, a small malfunction in hormones could lead to you having a Y chromosome and still being female in all meaningful ways).
Gender is exponential MORE messy, mainly because it's the kind of concept only academics would talk about. If you think about it briefly, it doesn't make any sense to just say "there are two genders, male and female" because that leaves out trannies, hermaphrodites, eunuchs, etc. If you expand the number of genders to include each of those, there will STILL be people who can't be categorized due to rarer and rarer genetic anomalies. And then there's the question of, are gay men and straight men the same gender? How about man-whores and prudish men?
It really gets to the point where saying there is only one gender encompassing all humans, is as reasonable as saying there are 551 genders, to account for every possible permutation of sexual proclivity and genetic disorder, or as saying there are 6 billion genders because no two humans can be said to have the same gender. I'm really failing to see where the concept is even useful except as intellectual wank fodder for humanities professors. Yes society should adapt to the existence of gays, transsexuals, whatever else. I don't really see where trying to haggle out a definition of gender is useful there.