"Atwood was also inspired by the Islamic revolution in Iran in 1978–79 that saw a theocracy established that drastically reduced the rights of women and imposed a strict dress code on Iranian women, very much like that of Gilead." - https://en.wikipedia.org/wiki/The_Handmaid%27s_Tale#Composit...
From Atwood herself (https://lithub.com/margaret-atwood-on-how-she-came-to-write-...)
"The deep foundation of the United States—so went my thinking—was not the comparatively recent 18th-century Enlightenment structures of the Republic, with their talk of equality and their separation of Church and State, but the heavy-handed theocracy of 17th-century Puritan New England—with its marked bias against women—which would need only the opportunity of a period of social chaos to reassert itself."
Of course all fundamentalist oppressive branches of religions, be it Christianity, Islam, Judaism or whatever, converge to similar shapes.
Atwood was worried about trends in the US and imagined a world where the earliest conservative Puritan Christianity -- that she considers a foundational part of America -- made a comeback. So no "gender equality". The early Puritans didn't behave "like Islam", any similarities are a result of a convergent evolution of sorts; their sins are entirely their own: fundamentalist Christianity. Atwood said much, that these were faults of the West she was describing.
I'm all for Death of the Author, but the specific claim I refuted was about what Handmaid was intended to be about (not other valid interpretations) and only the author can answer that. And she did!
https://www.patreon.com/DarvishIntelligence/posts/handmaids-...
From Atwood herself:
"The deep foundation of the United States—so went my thinking—was not the comparatively recent 18th-century Enlightenment structures of the Republic, with their talk of equality and their separation of Church and State, but the heavy-handed theocracy of 17th-century Puritan New England—with its marked bias against women—which would need only the opportunity of a period of social chaos to reassert itself.""
"Like the original theocracy, this one would select a few passages from the Bible to justify its actions, and it would lean heavily towards the Old Testament, not towards the New.
[...]
Surely the Gilead command would have moved to eliminate the Quakers, as their 17th-century Puritan forebears had done."
"I made a rule for myself: I would not include anything that human beings had not already done in some other place or time, or for which the technology did not already exist. I did not wish to be accused of dark, twisted inventions, or of misrepresenting the human potential for deplorable behavior. The group-activated hangings, the tearing apart of human beings, the clothing specific to castes and classes, the forced childbearing and the appropriation of the results, the children stolen by regimes and placed for upbringing with high-ranking officials, the forbidding of literacy, the denial of property rights—all had precedents, and many of these were to be found, not in other cultures and religions, but within Western society, and within the “Christian” tradition itself. (I enclose “Christian” in quotation marks, since I believe that much of the Church’s behavior and doctrine during its two-millennia-long existence as a social and political organization would have been abhorrent to the person after whom it is named.)"