The SA government doesn't support Al Qaeda of course, but the government does heavily fund extensive networks of religious schools and charities that push a very intolerant and view of non-Muslims and non-Wahhabi sects of Iskam, to the point of preaching violence and repressive treatment. In countries like Pakistan these schools are recruiting and training grounds for violent groups. Whether this is a deliberate policy by the SA government or just the result of poor governance and oversight of these organisations and their funding is an open question, but the result has been a dramatic radicalisation of Islam in many of these countries, far more so than in Saudi Arabia itself. I think many Saudis would be shocked to discover how much Saudi money is being diverted to fund terrorism and preach violent Jihad and intolerance of others.
To your point on Iran, yes hey are in some ways an even bigger concern. Where Saudi Arabia is funding extremism largely by accident, Iran is doing so deliberately. Still, that is a question for dealing with Iran which is a separate issue. Unless you are arguing that it's OK for Saudi Arabia to fund radicals and terrorists because Iran does it? But I don't think that's what you mean.
It's pretty hard to believe that the Kingdom hasn't figured out this is happening and are completely helpless to stop it. They either can't or won't, but they certainly know who is doing it and the extent it is occurring.
However where the ideology being supported and promulgated does go beyond what they would consider acceptable, they just don't have and are basically incapable of the level of oversight and monitoring required to identify and address it. That occurs to far down the funding and management chain for them to be equipped to deal with it. So in reality their choices are switch off the whole thing - billions of dollars in funding for education, health and charitable causes across the Muslim world on which extensive programmes and hundreds of thousands livelihoods depend - or live with the downside while making ineffectual efforts to control it. From their point of view these programmes are doing vastly more good than harm. It's just a matter of relative priorities.
But is it not a known fact that the 9-11 operators were a) Saudi, and b) backed by the Saudi government?
I'm certainly happy to be proven wrong, but if I'm correct here, that seems a lot to me to fit in with the concept of "exporting terrorism".
a) yes, b) no. Saudi government's relations with Osama bin Laden and his network went sour in about 1990.
What is your definition of moderate? Moderate compared to what country?