Iraq. Learn from India's History.
The British delayed Indian Independence for almost 45 years by playing up religious fundamentalist sentiments. . In 1947 India was partitioned with the largest death toll and population transfer in recent memory.
The main architect of in first denying and then delaying the independence of the Indian sub continent was Churchill, eventually a great world war two leader of Britain . The vast majority of Indians were poor and uneducated and lived in peace in multi religious neighborhoods. The independence or self rule movement was mainly an intellectual one till Gandhi entered. If there was any kind of display against the British rule, it was crushed mercilesly.
This merciless use of force gradually led to greater opposition to the British rule growing into a mass movement by 1930's. British meanwhile raised the religion card and refused to leave till all religions agreed. Never testing the so called leadership through even local level elections till they had a division.
Eventually there was independence and partition and mass massacar and population transfer. Indai and Pakistan have been at odds ever since.
That is what is now happenning in Iraq. The only difference is that the major transfer of population between Shai Sunni and Kurds has largely taken place in the last 4 years, walls built and religious armies created. So there is relative peace for now.
I do not know the answer for Iraq but I recognise the problem.