Presumably it knows what it's doing so why should it want to stop?
Because the #1 threat to the power of the House of Saud are terrorists :).
Since 1777 there have been revolutions going on everywhere, one way or another. The ideologies have varied. But where there was not 'progress', some 'leader' used an ideology to validate their revolution. In E. Europe and Asia it was Communism, in ME it's one brand of Islamism or another.
Al Queda is very much against House of Saud and would want to overthrow them 'first', type thing.
It's a complex issue.
And family trumps ideology so you have a mixture of ideals which are supported and are more often than not contradictory.
The ruling family also uses religion to control the people so if it stops all support it will find it self under the bus rather quickly, so even the most moderate have to extend some support to the fringe elements.
What people seem not to understand that for the most part moderates in that part of the world as still antithetical to western values; the ones who aren't aren't moderates are extremists just ones who we share values with.
Also as mentioned "family" and keeping power is more important to the moderates than pretty much anything else. The House of Saud is huge, where you have 1000's people of the royal family all of which have immense power, wealth and royal privilege you'll have a full spectrum of opinions from princes that get drunk and snort cocaine off the backs of prostitutes in a Macao casino to hard core celerics.
But what they all care about the most is to keep their name, title, wealth and power.