This is a commonly held view among the punditry. But the author ignores the obvious counterexample: all the division in the 50s, 60s, and 70s such as over desegregation, civil rights, abortion, and the Vietnam war, despite higher rates of religiosity. You cango farther back: the civil war. America has always been deeply divided.
I think the obvious counter example is the fact that there's a lot of political extremism in the bible belt. The extremism seems to be more homogeneously distributed where lack of religion isn't.