You're attributing the current violence to conditions relating to the origins of Islam, which is not the case. Yes, Sunni and Shi'a have had differences from the very beginning, which have at multiple times lead to bloodshed, but it has not been a constant war. Certainly not for extermination.
If Islam did not seek to destroy the other religions in its territory (Jews, Christians, Hindus, Zoroastrians etc) or heterodox offshoots such as the Druze or Alawites, why would it seek to destroy other Muslims? Not to mention that historically, Twelve Imam Shi'ites (the majority) were uninterested in political power.
This form of Sunni/Shi'ite fighting started in the 20th century. In the early 1900s, the House of Saud, with the support of the Wahhabi movement took control of the Arabian peninsula. The Wahhabis are ultra-orthodox Sunnis who find Shi'a, Sufism or just about any interpretation of the Holy Qu'ran and the Sunna and Hadith of the Prophet that does not meet theirs completely heretical. They deported all Shi'ites, and banned the teaching of principles that do not agree with their view of Islam and Shari'a.
A few years later, after the fall of the Ottoman Empire, an Arab national movement began to grow. The foremost feature of this is secularism, a completely European concept. Look at national movements of the same time, in Germany, Italy and Spain. Adolf Hitler was hugely influential among Arab nationals, the Arabic translation of Mein Kampf was wildly popular. The Nazis liked that many Muslims (not necessarily just Arabs) could be easily swayed into hating Jews, France and Britain. The foremost national movement was Baath Parties, which arose in Syria. They added their own racist agendas, such as a hatred for Persians, who make up the majority of the Shi'ite population. A hatred for Persians turned quickly into a disdain for Shi'a, which became seen as non-Arab.
Now Saddam's Baath Party strongly differed from the earlier parties, but the basis is still there. If you follow the history, it doesn't flow very well. These events are only related to earlier Sunni/Shi'a fighting by twisting history, which is exactly what happened, for the profit of individuals, and not for the religion of Islam.
(edit: Jon was writing the same time I was, and covered most of the points I did.)
:master::master::master: