The short answer to your question is Yes, such a society is possible, but I suspect that the question behind the question is what such a society would look like, so I'm going to answer that in more detail.
I'm of the view that focusing on the nature of reproduction and extrapolating a culture fails to take into account the far more energy intensive aspect of reproduction; raising the child. This is (arguably) why marriage evolved from an anthropological perspective; raising a child (or children) takes a massive amount of effort and energy; women struggle to do it by themselves, but men want some surety that the effort they put into the raising of children is going to directly benefit themselves, genetically speaking. So, a contract is made whereby the man agrees to pool resources with the woman to raise her children, and the woman agrees that in return, all the children he's helping to support are his. If this contract is ubiquitously in place for all couples who procreate, then the discussion of reproductive rights of both the man AND the woman become redundant but we know we don't live in such a world and as far as the scope of the question is concerned, I digress.
In a culture where children are basically all vat grown (I'm going to use that term to differentiate between the artificial womb and a normal biological pregnancy; no offence is intended), the energy cost to the woman of gestation is negated. But, what about raising the child? Providing it with food, protection, and guidance? This is where the real cost of children is, as any parent, male or female, will tell you.
So, who ultimately raises the child?
Well, the answer is more or less the same as it has always been - the biological parents. In this case though, that could be any mix of gender really and as such, it's entirely possible that you'd see pairings that look suspiciously like marriage pop up even in a single gender society because the effort involved in raising a child will still be borne by those who contribute to the genetic heritage of the child in question because they are the ones to benefit from raising the child in the first place.
But, a note on some of your other comments - Yes, in a wartime situation historically it has been men and not women who have fought as soldiers. But, that fact doesn't justify the perpetuation of the myth of the violent male. In my experience, women can be (and often are) just as aggressive (if not more so) than men in many cases. The stereotype of a caring mother and indifferent father just isn't true and needs to be challenged at every level.
Men (on average) are larger and stronger than women, and that means that they tend to manifest their aggression physically. But, women can be just as violent, often inflicting emotional violence where they are not in a position to inflict physical violence due to a mismatch of physique.
By the same token, fathers (in my experience) love their children every bit as much as mothers do, again more so in some cases. The reason why this is not expressed the same way is that society sees the responsibility of providing for the family as belonging to the father, thus forcing him to distract himself from the effort of child raising with the effort of providing for the family as well.
This, ironically, is what is retarding modern feminism's advancement; the focus on rights has put those rights out of equilibrium with gender based responsibilities and expectations meaning that until the women's rights movements become women's responsibilities movements, they will struggle to make further progress, but again I digress.
The point of all this is that a child having two fathers, especially in a single gender environment, will in no way retard the development of the child. In point of fact, because having children is a conscious choice in such an environment, and can't occur by accident, children raised by two fathers in your world are probably subjected to even better levels of nurturing and guidance than modern children are.
Put even more simply, it is a mistake to confuse gender stereotypes and cultural expectations with gender based capabilities. Fathers are every bit as capable at being parents as mothers, and in your world, away from the current gender based expectations and responsibilities, would be more than capable of demonstrating that.
