While I can see how this manga could be supposed to be an commentary on today's stupid society and gender, the problem is that the world the story creates for this commentary isn't fit for this. I would even say that if it is a commentary, it comments on older society like 100 or 200 years ago, because it undoes so much of what society already has achieved today just to have a reason why there is a problem with Eve - Eve and Adam - Adam couples. And most of it is just hard to believe and it insults woman because they came up with this in the story.
The manga doesn't just enforce gender, it super enforces them as it reduces half of the populations freedom and value just because and everyone went along with it. That must have been one funny assigning ceremony when the system was installed.
If they wanted to exaggerate to make their point clear they should have done a better job with the backstory.
The world/setting is just poorly crafted and distracts to much from the main topic at hand, if there is supposed to be any. Maybe they just wanted a (baroque) setting and a reason for why two woman can have children and didn't bother with the rest.