"It strikes me as medieval, but then what we call medieval was Christianity before secular governments arose."
"Secular" only in the sense that the government was actually a separate entity. And, this didn't just arise, whole, out of some primordial soup ... it was the direct result of the Protestant Reformation.
I haven't seen any nation voting to go back to the divine right of kings, or even to reinstate an official religion. It seems that once people are free of religious coercion, they don't voluntarily go back.
I suspect the current infatuation with official sanctioning of religion, by a vocal segment of the Republican Party, is the primary reason why educated people tend to be horrified by the party.
It's a bit like what happened to the democrats with the peace movement. They found themselves attached to a winning party, assumed they were responsible for the wins, and proceeded to trash the party.
There is no inevitable conclusion that a Protestant religion leads to secular government.
Counter examples: John Calvin, Dr James Kennedy.