I read the book The Handmaid's Tale in the late 1980's. A disturbing story, but I enjoyed dystopian fiction back then.
Later, when our country went to war in Afghanistan, the Taliban looked to me like a real-life version of that story.
I don't watch TV, so I don't know anything about the TV series. But, in the book, "Gilead" was supposedly brought on by a combination of Christianity and feminism. But you're right - it's more like old-school Islam than either Christianity or feminism.