The Shite-Sunna dispute is not considered as part of Islam. This is only part of the history of Islam. The period of revelations of Islam came to end with the 5:3 verse of Quran what was mentioned by Mohammed (PBUH) in his last sermon what he delivered before his death:

This day have I perfected your religion for you, completed My favour upon you, and have chosen for you Islam as your religion. (Quran 5:3)

So, whatever happens after this verse it cannot be considered as part of Islam.

There are volumes about the formation of Shite-Sunni sects however briefly the following issue happened. After the death of Mohammed (PBUH) dispute started about his heritage. In other words: who can be the caliph? The followers were divided into two main groups. One of them said that the caliph has to come from the household of the Prophet (PBUH). This group is called Shite. The other group said that lineage of household of Mohammed has nothing to do with the power. Only Sunna, the tradition and prescriptions of Mohammed have to be followed. These are the Sunnis. However, both sects follow the same Quran and regard Mohammed (PBUH) as Prophet. So, the difference between them are the power and the control over Muslims. This subject cannot be considered as part of Islam. In fact, it is pure politics what always caused wars against them for gaining the power and not because of eliminating the differences between doctrines. Even today the situation is the same. If politics is the dividing line, Saudi Arabia, Israel and USA represent the Sunni part, and Iran, Russia and their allies represent the Shite side. Yes, I know that Israel, USA and Russia are not Muslim countries but this is how politics works. Before the Islamic revolution in Iran Reza Pahlavi shah ruled Iran and he was ally of US. That time there was no Shite-Sunni dispute! And maybe after 50 years the axis what divides shite and sunna will be in quite different place. But no matter what dispute raises between Muslims it goes against the will of Allah:

And hold fast, all together, by the rope which Allah (stretches out for you), and be not divided among yourselves; and remember with gratitude Allah's favour on you; for ye were enemies and He joined your hearts in love, so that by His Grace, ye became brethren; and ye were on the brink of the pit of Fire, and He saved you from it. Thus doth Allah make His Signs clear to you: That ye may be guided. (Quran 3:103)

Yathrib (later Madina) was torn with civil war and tribal feuds and dissensions before Prophet set his sacred feet on its soil. After that, it became the City of the Prophet, Medina and unmatched Brotherhood and pivot of Islam. This poor quarrelsome world is a larger Yathrib. Can we establish the sacred feet on its soil and make it a new and larger Madina? This aya calls for Unity of Muslims and calls for Brotherhood of all who make good deeds, want peace and prosperity.

I know, that some very clever comments will complete my article and they will enter into the details of uncountable blames against each other due to the fake Hadises and different traditions in practice however the most important issues should not escape from our concern. Even Shite follows sunna and even the Sunni respects the household of Mohammed (PBUH). So, the whole debate is barren and in long term when thinking of Muslims will reach a more rational stage it will lose its significance.