I reread Handmaid’s Tale a few months ago, remembering the movie version in the process.
ISTM that the movie version was heavy on the religion, making religion the heavy.
But the book was quite different. Religion played a part in the handmaid’s plight because it was s religious war that resulted in the sterility of most of the female population. Religion was the backdrop of the victorious society.
But the slavery of the handmaids had nothing to do with religion; it had to do with the fact that they were the owners of a very valuable resource — — fertility — and the handmaids were enslaved (essentially) so that resource could be stolen from them.
Simply put, RELIGION was not given, if I recall correctly, as the justification for locking up and using the fertile women as breeders. It was simply that they were fertile, and the government authoritarian. That was enough.
Certainly, nobody would argue that the only authoritarian governments in history are religious ones. That thought has no legs.
I don’t know if Atwood ever commented on her thoughts when writing the book, but I think she would take issue if her work was characterized as “See what happens when religion takes control”.