Southern Iraq, significantly, did not convert to Shi'ism under the Safavids. While there did exist significant minorities, most prominently located in the shrine cities of Najaf and Karbala, the majority of the countryside as well as the nomadic tribal groups (which made up more than 50% of the population), were Sunni. This changed starting in the late eighteenth century, and picked up speed during the nineteenth.

Najaf and Karbala greatly increased in significance following the collapse of the Safavid dynasty in the early eighteenth century, as scholars fled from the chaos in Iran. Then, Wahhabi attacks on these cities at the beginning of the nineteenth century led to a greater emphasis on communal organization and an increase in the authority of the Shi'ite religious leaders, who set about establishing alliances with local tribes. Both cities developed as major market towns for regional trade. In 1831 the Ottoman government began a program of settling tribal groups and turning them into productive farmers, as well as infrastructure projects which changed the route of the Euphrates and increased the area of cultivable land near Najaf and Karbala. As the tribes settled, they maintained their links with the Shi'ite authorities. Settling meant giving up their old way of life and adopting new identities for themselves, and their close relationship with the shrine cities led them to convert to Shi'ite Islam. Thus it was the process of tribal settlement (tribes had formerly been the majority of the population) which led to southern Iraq becoming Shi'ite, a process which was still ongoing by the time of the British takeover. Thus while Shi'ites have had a presence in Iraq since the very beginning, they did not make up the majority of the population until very recently - less than 100 years ago.

Nakash, Yitzhak. “The Conversion of Iraq’s Tribes to Shi’ism.” International Journal of Middle East Studies 26 (1994): 443-463.

Southern Iraq was Shia from a very early date, with possibly one of the earliest and longest continuous Shia communities in Muslim history. The birth of Shia Islam is deeply rooted to Iraq: the Caliph Ali made Kufa his capital, south of Baghdad; his tomb is enshrined in the city of Najaf, located squarely in the south; his son, Hussein, died in battle in Karbala, near Kufa. Ali and Hussein are two of the most central figures within the Shia theology.

From early times, communities of Shia predominated down southern Iraq and along the Arabian coast of the Persian Gulf (where my expertise lies). When the Safavids converted to Shia Islam, they encouraged the migration of Shia clerics from Bahrain, Lebanon and Iraq to essentially create the religious infrastructure for the new Shia state, and it took time before strong Iranian Shia traditions and seminaries took hold (with the establishment of schools in Qom for instance). The Safavids were a hugely important state for Shia Islam, but they were indebted largely to Arab Shia traditions without which the conversion would not have been successful.