Sunni dominance over Shia was not settled until the high Middle Ages

Evidence

The Sunnis and the Shi ites were by no means the only schools in early Islamic history, but they are by far the most important, with Sunnism as the dominant, mainstream form of Islam, and Shi ism as the most powerful and challenging of the alternatives. Sunnis and Shi ites faced each other in all the early civil wars and struggles, and for some time the outcome of the struggle between them for leadership and domination of the Islamic world was far from certain. It was not until the high Middle Ages that the Sunnis were able to establish themselves at the prevailing form of Islam, while the Shi ites, more and more, came to be a minority associated with deviant doctrines and political dissent. — Bernard Lewis, From Babel to Dragomans, 1426

Categorization

• QUESTION: What exactly shifted in the high Middle Ages — conquests, institutional structures, or theological consolidation — to tip the balance decisively to Sunnism? Worth chasing.
• corroborated: 2 independent passages support this claim — Bernard Lewis, From Babel to Dragomans: Interpreting…, 1426