I wouldn't have seen it again or raved about it myself if I felt like it was blunt, didactic, and/or overbearing thematically. With the exception of the bag of seeds and maybe a couple other moments/lines adding up to MAYBE a full minute of material, I think it was handled very well. I nevertheless do think the themes were quite explicitly there; they were just easy to look past (or at least not dwell upon at length) given the frenetic pacing & amazing action.
...yeah, but that short conversation is the one that involved the bag of seeds. And she explains - "back then, everyone had their fill" (or something like that) - back then, you didn't HAVE to kill people. That was before (drumroll) ...the world was killed. By men.
"Who killed the world?" is rather explicitly painted on the walls of the breeder place when Joe barges in and discovers them missing, and is again recited as a line of dialog. I'm fairly sure the answer is: men. Also on the walls: "Our babies will not be warlords" - I think you're conflating slavery in the abstract with the very specific form of reproductive slavery - to me, a stand-in for reproductive rights in general - that's actually playing out. Give it some thought.
I think the "green place," and the bag of seeds, and the many mothers, and the emphasis on reproductive rights, and the "Who killed the world?" refrain, and the depiction of men as (almost unilaterally) unreasonable and selfish religious nuts, and the depiction of women as (almost unilaterally) reasonable and compassionate individuals uniquely capable of seeing past Joe's BS and having emotions and what not adds up to something a bit more than just "bad guys vs. good guys," as you've laid it out. I don't think it's a stretch - I think it's rather explicit, actually - but like I said, I also think it's handled really well, offers a refreshing change of pace for this genre, and makes it all feel a bit new (in addition to the stylized, fantastic directing) without really proselytizing.