It is actually quite the contrary, and depends on how you look at it. But I am saying that you got to look at the geopolitical map of the region and understand which country support each other:
Saudi Arabia: a Sunni-dominated kingdom, very strict with Islamic codes, a lot of restrictions for non-Muslim and woman alike. They are very troublesome, but is a very close USA ally.
Iran: a Shiite ruled theological Republic, Islam is the main ideology of the country, however there is much more freedom for women and non-Muslim, including Iranian Jews (which get reserved seat in the parliament). However, they are much hated by USA.
Iraq, Syria, and Bahrain is quite an irony. The natural balance in Iraq has been restored by US invasion, so the Shi'a majority now rules the country. Syria is on the wait. While Bahrain, the Shi'a dominated country, but under Sunni rule, is still unknown. The last major protest was violently silenced with the help of Saudi Arabia.
Now about the Sunni-Shi'a thing. I never knew they were such a serious issue to predominantly Sunni Indonesia until I saw and heard it on my own. So my typically liberal best friend, who is a Muslim and have a quite deep knowledge in it, but love anything hipster and somehow enjoys pork chops. He has a seemingly bitter view of Shi'a scholar views. I can't really fathom that even the most liberals of Sunni people can reserve such hatred towards seemingly bunch of innocent people.
The problem mainly lies in one of the five pillars of Islam itself: that you have to testify that Prophet Mohammad is the last Prophet of God, and there is nobody else. In Shi'a, this confession sentence is added with reference to Imam Ali, one of the first Caliphs, cousin of Mohammad, which married one of Mohammad's daughter and according to Shi'a disciples, are the legitimate Imam (spiritual leader) of all Muslims. So much praise goes to Imam Ali, that many Muslims questioned whether the Shiites worship this figure, which an act of heresy in Islam teaching.
Many regular Muslims doesn't want the Shiite to refer themselves as Muslims, since the Sunnis regard that the Shi'a teachings are misleading. Last year, there was a riot in one of Indonesia's remote village. The target was a Shi'a mosque, razed and burned to the ground, because they are accused of spreading false Islamic teachings.
Recently on my Facebook page, some of my friends started to discuss about Shi'a teachings spreading to Indonesia, due to our ignorance with Iran's seemingly defiant attitude towards Western hegemony. They talk a lot of how Shi'a followers tried to blend-in in regular mosque and how their prayer book contains no reference at all to Mohammad (as the last Prophet), but only to Ali and his family. And about how they avoid discussion by being taqiya (pretending to conform).
I never regard the conflict seriously, since I never experience it life, but when I saw one Shia family house being surrounded by angry mobs, now I realised. Probably it is not just the Syrian people unleashing whatever they hate about Al Assad, but probably their religious fervor as well.