The Saudi government is not Islamist, nor does it support Islamists. Since the collapse of actual Islamic government, regimes with majority Muslim populations have taken two roads;
1. Declare themselves a secular state and stomp the heads of anyone who opposes it.
2. Run a secular state, but declare themselves an Islamic state because they'll get their heads stomped if they don't.
Over the last half century many of the overtly secular regimes have appeased the Islamists and wider Islamism in the public by making psuedo-Islamic declarations and legislation; Muammar Gaddafi, Saddam Hussein, Bashar Al Assad, Hosni Mubarak, etc.
On the other hand, the Saudi regime began as a nearly puritanical Islamic state because it needed the Wahhabists. Since then it has moved away from Islamism, but to keep from being overthrown by a public that demands Shariah, they've made mouth pieces of the clerics and scholars because if the mosques approve the masses will not differ.
Outsiders see that the Saudi government funds mosques around the world, but they're selling rat poison from ice cream trucks. The same is true of the other GCC monarchies.
There is a reason the Saudi royalty has faced multiple coup attempts led by members of the elite, Osama Bin Laden and his brother are representative of a wider discontent that reaches from the bottom to the top of that society.
I remember being in Damascus and walking to the Christian Quarter. It struck me how difficult it would be to defend against a baying mob. No wonder the Christians are supporting Assad. Most of them if not literally would have personally met and assisted Christian refugees from Iraq. They know what will happen in the event of a chaotic overhrow.
While doing some hardcore Jew naming today on a nerd forum full of skinny fat pasty white liberal betas, I've come to the realization that the grand strategy USA/Israel/NATO is that collective of failed arab states not unlike Somalia is preferable to a semi modern, highly centralized one like that of Assad's Syria. This is the ultimate wet dream of the neo con Jews I think. Destabilize Arab states that are hostile to Israel, embroil them into a perpetual civil war and keep it that way. Forever.
For example, Somalia has been a failed state for the last 20 years and hasn't posed a serious military threat to its neighbours since the 1970s when it had the second largest army in Africa after Egypt and almost captured the capital of Ethiopia during the Ogden war (until the Soviets and Cubans intervened to save Ethiopia). Since than the Ethiopians have been intervening, playing off tribes against each other, making sure that Somalia never gets back on its feet.