In fact I don't think "The Handmaid's Tale" really makes sense without the context of the AP feminists. Gilead comes about, as I understand it, because the AP feminists think they can use the Religious Right to achieve their goals and unsurprisingly that goes badly for them. AP feminism doesn't even exist when "Left Hand" was published.
But maybe that’s just post-hoc rationalization for a reactionary stance, idk.