Careful where you point those fingers, FRiend. Protestant churches were and are at least as "integrated with the state" as the Catholic Church ever was.
Protestants have had their hand in statism too, but less tenaciously than the RCC before them. (England’s Anglicans and Scotland’s Presbyterians are today only ceremonial heads with no legal power over affairs of state.) Evangelicals (e.g. Baptists and Amish) that are not considered part of any Protestant mainline have typically been averse to statism from the start.