I think it may be accurate to say that the spirit of the OP suggests a liberal(in the classic sense) Saudi Arabia, at least in cultural and institutional terms. Ideally, one wouldn't have to identify and mess around with thorny religious development PODs.
With that in mind, might it be possible for an early 20th century POD lead to a post-Great War pan-Arab monarchic federation, with the Saudis as the titular head? I'm imagining a kind of super-UAE across most of the Arabian peninsula, save perhaps a small French christian-Lebanon enclave, or some kind of greater Kurdistan, etc. The idea behind a federation of this type is to force greater power-sharing and diversity of institutions across a broader population and economic base. While oil would end up a massive part of the economy, and drastically affect social affairs, federal subunits within this "Saudi" Arabia might do better in managing this income, while oil-poor areas gain spillover benefits of being within the same nation-state.
If we postulate that this Arabia includes Palestine, the dominant theme of the Middle East might revolve around an Arab-Persian dynamic. This contrast, while potentially volatile and violent, is less likely to involve the West or implicate western ideals as problematic.
Further, (butterflies permitting!) a decentralized, diverse, and relatively conservative Pan-Arabia is not going to be particularly attracted to European viruses of revolutionary fascism, socialism or communism; even if elements of society find such ideologies attractive. For basically the same reason, the social construction of this Saudi Pan-Arabia isn't going to be particularly friendly to the Soviets on any ideological or principled basis--even if poor relations with Persia/Iran or Turkey push Arabia into the non-aligned camp.
Finally, a Pan-Arab (Saudi) Arabia has a strong base for positive nationalism based on an "Arab" sense of identity, emphasizing historic achievements and cultural richness of previous "Arab" civilization. This kind of nationalism cuts across the peninsula, unlike more divisive religious or tribal identities that in this case are (generally) adequately represented or governed by local/regional political subunits.
Though the analogies are quite imperfect, Malaysia, Morocco and Turkey somewhat resemble (in myriad specific ways) the outcome of this Saudi Pan-Arabia I'm imagining.
Is it ASB? Nearly so?