People fight over a lot more than ideological differences. By FAR the most common reason for aggression is greed. One country may have enough resources to be comfortable, but they could be even MORE comfortable if they took some resources from their weak neighbor.
Also, the lines would not stay neat and pretty beyond the first generation. Someone who likes Country A's system may have kids who don't. And those kids may not want to move to the country "designated" for them and instead turn their "home" to what they view as the "correct" method.
Hell, we almost have that now in the US. Liberals are most dense in California and New York and Conservatives are most common in Middle America. But the ones who don't live in the "correct" areas for them don't just up and move. They try to "improve" their home instead.