You had it right with the civil war. Except instead of north v south it needs to be republican v democrat. You don't need a war really, just a way of agreeing how, why and which states will be democrats, and which will secede for the republicans and become the new nation of Elephantasia, and facilitate the movement of about 50% of the population to move to the country of their choice (voting allegiance). So you would have a secular, democratic America and a republican theocracy and they can go their own separate ways.