It is popular nowadays to talk about a conflict between Sunni and Shiites or between Iran and Saudi Arabia. I suspect those conflicts are exaggerated. Consider the following:
- After the Iranian revolution Iran promoted Islamist revolutions everywhere in the Arab world. They didn't seem to care about the Sunni-Shiite difference.
- Just like the Gulf States Iran spends a lot of money on promoting radical Islamist goals. Often they support the same goals such as Hamas. Hezbollah too was until recently generally seen positively in the Arab world.
- Saudi Arabia and Qatar supported the uprisings in Tunisia, Libya and Egypt. They supported and still support Islamist organizations that want to establish an Islamist dictatorship. Yet this didn't stop those countries from initially seducing the West to support the uprisings with the claims that they wanted democracy.
- This raises the question how real the Saudi hatred of Iran really is. It might just as well be another insincere excuse to get the US involved in Syria.
- At the moment it appears that Qatar and Saudi Arabia are divided on Egypt. With Qatar supporting the Muslim Brotherhood and the Saudi's opposing it. However, the Saudi's traditionally support the Salafists. And while the Salafists initially supported the military they seem now turning towards the Brotherhood.
- Morsi initially opened up towards Iran. Later the relationship cooled but interestingly after the recent military take-over in Egypt this was condemned by Iran.
- There is a kind of feud between Saudi Arabia on the one hand and Hezbollah and Assad on the other because the Saudi's suspect them of having been involved in the murder of Hariri. Hariri was very close to the Saudi royal family and had the Saudi nationality. This too has little to do with sectarian issues.
So in my opinion spreading Islamism goes above nearly all other issues as the main motive of the Gulf States.