Excluding a modern, industrialised nation-state, the only way that this would be possible would be in a hunter-gatherer society--the survival of the group is paramount, so egalitarianism prevails; while gender associated divisions of labour do crop up to some degree, there are no actual roles in this regard per se. For example, with the Aka peoples of central Africa, everyone hunts, gathers and shares resources, and though men may tend to hunt more, women and children often accompany and assist them.
Other than that, this is largely impossible.
Once agriculture develops and the society settles, it's only a matter of time before patriarchy also develops. Both sexes may be fully eligible to hold any position in society, but anatomy makes this irrelevant. Human males just tend to be larger and physically stronger than than females, so they'll naturally make better candidates for specialised activities and roles that require a great deal of strength, especially when it comes to soldiers and warriors. As there is no birth control, women are also going to be often incapacitated by pregnancy and nursing.
Even if you had a fully egalitarian society, the birth rate is going to be very, very low, as women are not going to want to risk death in childbirth, especially if they happen to hold very crucial positions in society. Add to this infant mortality rates, and you have a pretty small population. This means that the society in question will be rather slow to adopt any forms of technological innovation, as their current mode of production easily enough serves their needs and numbers.
And, even if you had a military recruiting pool of, say, fifty males and fifty females, in the village, odds are, there will be more males in this population that better fit the criteria for a warrior, inevitably leading to the role becoming a male dominated one--and that's just one example.
Compare this to a patriarchal society, where men fill all the roles of leadership and protection (i.e. soldiers) and the population is far greater, due to a higher birth rate. When it comes to competing for resources, they'll definitely have an advantage over any purely egalitarianism society, as they have both the numbers and strength to seize what they need, as well as more of a reason to adopt technological (particularly agrarian) innovation in order to accommodate a growing population.
My point is, even if a 'gender-blind' society existed, it probably wouldn't last very long in the long run. And, even if it did, given very fortunate circumstances in terms of isolation and available resources, such a group would probably be limited to simple farming societies, without a great deal of the need for the specialised labour complexity that the OP asked for.