Yes, it's "about a Christian theocracy" in the sense of "what if a Christian theocracy behaved exactly like an Islamic one".

"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...

Nope. A Christian theocracy of Puritan values.

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."