Correct. Religion was the reason given for the war and the “split” between the two “sides”.
From THAT POINT, the matter of religion was not partciularly relevant; it was because the fallout from the war had rendered 99% of the women sterile, and therefore the most valuable asset in that nation suddenly became fertility.
And government just did what governments do; they move to control the most valuable asset.
After I wrote that, I *did* read some commentary that Atwood herself had provided on the book, and quite right, it was not religion that she was commenting on, according to her.