What the flock is that?! Sounds like some dadgum romance novel but written by a lesbian!
I read the "handmaiden's tale" in college. I thought it was entertaining for being so unbelievable. The idea that Jerry Falwell types taking over the US is far less likely than watermelon atheists. OR, in more recent times, Islamofacists. Even in my liberal youth, I couldn't imagine a civil war with Baptists bothering to blow up Quakers and Amish. If anything, they'd tell the Amish to do more breeding and ignore the Quakers.
Methods to drive up the birth rate would best be done by massive tax credits for parents, not raping fertile women. The stress of confinement would decrease her fertility, not increase it. And passing women from man to man until she got pregnant would increase the risk that the infected men would give the precious fertile ones a disease.
If anything, the world it paints already exists behind the burqa. The violation of womens' rights is here and now, but it's behind the Veil, not the Bible belt.