Wahabbism is prevalant, and they take their role as “Keeper of the Two Holy Mosques” incredibility seriously.
(so they export it to the west unopposed).
Much of what the family does is to prevent this by placating, buying off, balancing, and coercing the varied elements of the population. This constrains them politically, because there are red lines they dare not cross.
(so they export it to the west unopposed).
...if the KSA becomes an active Islamic revolutionary state,
They're already there - exporting Islamic expansionist ideology into non-Islamic countries unopposed and abetted by "progressive" elites, and sending their agents to populate wahabbi mosques (cells) in MY city.
...they would quickly gobble up the Gulf states and Jordan would not last much longer. They could effectively shut down the Oil trade, close the Red Sea and force trade to go around Africa, and likely start a major war that makes the Iraq war and Syrian Civil War look like a tiff between toddlers.
They could do that if unopposed by real countries (with real presidents), and until they ran out of mercenaries.
The KSA is not a revolutionary Islamic state, it is a traditional establishment one. The exporting of religious (not revolutionary) ideology is part of their internal safety valve. The crazies become someone else’s problem.
The Saudis, while a pain in the ass, essentially accept and operate within current international systems. They need customers overseas for their oil and also need thousands of western technicians to help them get it out of the ground. (As an aside, I flew from Frankfurt to Bahrain on business last spring, the flight stopped briefly in Damman, KSA, and dropped off 75% of the passengers, western men and some women(!) who work there. It’s a daily flight so you have 200+ westerners going in and out daily).
If the Saudis were overthrown, a revolutionary Islamic Arab state in former KSA along the lines of AQ or Daesh/ISIL/ISIS would not function like that. They would seek to expand influence by force. Geography matters, the Kingdom dominates the Arabian Peninsula, which dominates both the Red Sea and the Persian Gulf. If that area becomes non-permissive, we have a severe problem. Logistic times triple as bulk cargo has to go around Africa, and we have to rely on the Gulf states that are both small and subject to the the same pressures that Saudi Royal Family were. The incoming Administration would have the will, but actually sustaining a campaign would become a stone bitch.