you realize that split is still a pretty big deal to them right? We are in the political forum, one of the biggest fights we have here, and in the rest of the country, is exactly that "minor" disagreement the Muslims have: who leads them.
they have been fighting each other since the very start. Ali was assassinated by the Sunni, and there were wars between the multiple different wars between caliphates based purely on who was in charge of the religion. The Sunnis won early which is why they make up most of the population now.
there is little antagonism because the Shia make up such a small percentage of the total, and most of their population is either in Shia controlled territory or other secular nations. there is very little interaction between the two, and when there is it is typically dominated by one of the other and the locals just have to accept the rule. it is not a situation of "separate but equals" and more of "you stay over there and we will tolerate you"