Scandinavian countries (+ UK and Netherlands, which seem to cluster closer with them than with the rest of EU) top most indexes of "economic freedom" / "ease of doing business" etc. And they still have monarchies over there, with state-church separation happening only recently, or not yet. And Sweden has large private school system etc.

Or they have huge taxes, very comprehensive welfare state system, allow gay marriage or some other type, have a lot of out of wedlock marriage, extremely high rate of women participation in workforce etc.

Depending on which features you focus on, you can make them appear "extremely liberal", or "extremely conservative" by US metric. It will be stupid categorization either way.