"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!