we need a parting point way farther back so that modern Iran does not regard the coasal regions as traditional part of their nation or better still popular culture in 'mainland' Iran/Persia does not regard the people of the coast as 'true' Persians.
I suggest: Before Islam, city-states at the western part of the gulf were much greater naval powers and traders and developed strong ties with the cities on the western shore. Come the Islamic conquests, they spread the faith to the west and so the western shores of the 'Persian Gulf' become Sunni while mainland Persia becomes Shi-ite. Eventually the western shores and eastern cities form a kind of 'hanse' or Common sea economic union'. The eastern city-states just like the western ones become emirates, traders intermingle and intermarry and soon the whole coast of the increasingly obvious misnamed Persian Gulf is Sunni Arab in culture and politics.
Eventually as the new Persia rises in power it may at several times conquer or occupy at least part of the eastern shoreline. However it become pretty clear that the region has now become Emirate-Arab instead of Persian and eventually Persian rulers will leave the coastline to the 'native' population and instead focus on conquering India and Pakistan.