In Denmark when they want to make fun of American self-importance, they call it "guds eget land" or "God's own country". I've never heard the expression in English.
I've heard it used referring to New Zealand (by NZers, although often now abbreviated to just "Godzone"). The equivalent term we'd use to make fun of the US is "land of the free".
I'm from the American south, we refer to any rural area where people are more self-reliant and the land is not developed as "God's country." It doesn't have much to do with how religious the area is or how many churches are there.
The expression "God's country" is not that uncommon, and maybe used ironically or just without any particular expression of religiosity. Usually I've heard it used to refer to an area pleasant to live in or visit.
I've heard both “God’s Country” and, though somewhat less frequently, “God’s Own Country” used to refer to parts of America, particularly the rural Midwest and/or Bible Belt.