What is the major ideological conflict within Islam?

The root of most of the ideological conflict within Islamic religion stems from a difference in belief of who was and is the appropriate successor to the Prophet Muhammad. In fact, the greatest divide in Islam is between the Sunni and Shi'a sects of Islam.

Sunni Muslims, who make up about 85% of the worldwide Muslim population, believe that the successor to the Prophet Muhammad as caliph (the highest religious authority) was his father-in-law Abu...

The root of most of the ideological conflict within Islamic religion stems from a difference in belief of who was and is the appropriate successor to the Prophet Muhammad. In fact, the greatest divide in Islam is between the Sunni and Shi'a sects of Islam.

Sunni Muslims, who make up about 85% of the worldwide Muslim population, believe that the successor to the Prophet Muhammad as caliph (the highest religious authority) was his father-in-law Abu Bakr. Shi'a Muslims constitute about 15% of the worldwide Muslim population and believe that the rightful successor was Ali Ibn Abi Talib, the cousin and son-in-law to the Prophet Muhammed. 

This divide is not just about who succeeded Muhammed as caliph, but also about how the successors are chosen. Sunni Muslims believe that leaders should be elected by a consensus of the Ummah, or Muslim community. Shi'a, on the other hand, assert that before his death, Muhammad appointed his son-in-law Ali and his descendants as the succeeding caliphs.