Part of the issue with the question is that Islam as an orthopraxic religion (i.e. emphasizing correct action, as opposed to orthodoxy, emphasizing correct belief) there isn't as much of a distinction between theology and politics as one might expect. I'd go so far as to say that there still isn't as much of a theological split as one might expect.

That being said there are probably two key periods. The first is when Sunni religious law starts to really be codified, both as an independent scholarly project and also as a movement by some of the early Abbasid caliphs to try and create an imperial legal framework out of the religious law, starting around the time of Harun al Rashid. This is also around the time that Jafar al-Sadiq, the 6th Shia imam, is completing his equivalent work of jurisprudence.

The second time period is the "Shia Century" of the 900s, when the Fatimids ruled in greater Egypt and the Buyids in greater Persia. At the end of the 9th century the last Shia imam of the twelvers went into "occultation," supposedly being hidden for his protection. Then in the 10th century he went into the "greater occultation" where he did not appoint a successor, but will supposedly return as a major figure in Shia eschatology. This period marks the completion of Shia practices and beliefs.

By the end of the following couple centuries, and the so-called "Sunni revival" both Shiism and Sunnism more or less resemble what we see today.