I'm not actually sure how common it was for the government to intervene in families' home lives, even, say, at the height of the middle ages or the Byzantine empire. That said, to whatever extent it did happen, it was wrong, and the Catholic church acknowledges as much these days.

On the other hand, I think the history of humanity, which involves nearly universal belief in some flavor of divinity, is all-but-conclusive proof that your second point is incorrect. That doesn't mean the x-theists are right: just that religion is quite obviously the default state of humanity, and irreligion is the exception.