I agree that Eden and her family were more than likely of a Gilead mindset even before Gilead was established.
People won't have become Gilead believers overnight. The discontent in modern, liberal America will have been there for people like Eden's family for years before Gilead was established, they will have been a religious, possibly pious, conservative family well before the coup which saw Gilead established.
They probably welcomed this because they will have been living a similar way anyway even before. Not as extremely as now, but with similar values.