Final answer:
The main differences between Sunni and Shia Muslims in the Abbasid period revolved around leadership succession, religious interpretation, and authority, with Shias emphasizing the Prophet's bloodline through Ali for leadership.
Step-by-step explanation:
The differences that separated the two main sects of Islam, the Sunni and the Shia, during the Abbasid period encompassed disputes over the leadership succession, differing interpretations of religious texts and practices, and the broader question of religious authority. Initially, the early Shia supported the Abbasids because of the requirement that the caliph be from the Prophet Muhammad's family. However, as the Abbasids started overlooking Ali's kin in the succession, the Shia began to articulate the principle that authority of the imam should specifically pass through the Prophet's family via Ali and not through others less closely related. This doctrine became a core division between the Shia, who believed leadership should remain within the Prophet's family, and the Sunni, who did not see this as a requirement for Islamic leadership.