Thats a bit of a simplification of European history. There were both catholic and protestant states within the Holy Roman Empire and each tolerated the other.Most people reading this thread probably already know this, but just in case...
A reasonable historical parallel for current relationships between majority Sunni and majority Shia Muslim states is the relations between European Protestant and Catholic states in the 1600's and 1700's. A few of them worked together, but mostly they existed somewhere between hostility and active warfare. In the modern day, most of the warfare is by armed proxy groups (Hamas, Hezbollah, ISIS, and these folks, who were news to me).
During that period of European history the priority was to maintain the balance of power in Europe. The Bourbon and Hapsburg monarchs each tried to claim additional kingdoms as dynasties rose and fell, and successful claims would create one dominant state. Alliances formed and fell between Prussia, Britain, Spain, France, Austria and (orthodox) Russia together with Sweden, Piedmont, Swiss Federation and other smaller states. At one point the Ottoman Empire was involved in alliances with Christian states. These wars sometimes spilled over into India and the Americas. Religious issues were far less important than the pragmatic issues of trade and maintaining the balance of power.
In todays middle east we have an Iranian theocracy which sees itself as the descendants of the cultured Persian Empire. They look down on the Arabs, who they see as grubby desert tradesmen. The unresolved Palestinian issue gives focus for each of these groups and their national agendas.
Iran’s agenda is to become the regional superpower. It plays the religious card very skilfully by using the fundamentalist Revolutionary Guard to project its influence in a number of countries. I don’t see the Sunni states as having a religious agenda. They seem more concerned with containing Iran.