Our relationship with Saudi Arabia is simple. They play lapdog for the petrodollar, and we not only turn a blind eye to everything they do, but even provide them weapons and other support in their endeavors. The only thing that would ever cause us to reevaluate our relationship with Saudi Arabia, in the fashion you imply, is if one of the never ending Rumors of Saudi Arabia transitioning to settle oil contracts in e.g. the yuan became true. At that point expect us to suddenly decide Saudi Arabia is a huge violator of human rights under the rule of a despotic monarchy and is in desperate need of 'democracy' and 'regime change.'
This whole relationship makes all the Rumors of the Sauds swapping to the yuan all the more intriguing. If that ever did happen our response could well trigger something like a worldwide Cold War. China and probably Russia would likely have an obligation of support for Saudi Arabia, America would pull in NATO and the world would likely split along one side or the other. For that matter Saudi Arabia is also not like Iran, Iraq, Syria, Libya, ... . Saudi Arabia itself is now world's third largest spender on defense in raw dollars - and #1 in the world by percent of GDP. 10% of their entire GDP goes to defense. By contrast, we spend about 3%. On top of that Mecca and Medina reside within Saudi Arabia. Propaganda would be strongly on the side of the Saudis who would portray an attack on them as an attack on Islam.
>China and probably Russia would likely have an obligation of support for Saudi Arabia...
I doubt that. In the KSA - Iran cold war, China is squarely in the Iran camp. Personally, I don't even think they side with Iran because we support The Kingdom. Rather I think they side with Iran because the more sanctions we put on Iran, the cheaper the oil and gas China can get out of Iran becomes.
But yeah, there is pretty much zero chance that China supports KSA. Even if KSA wanted to use the Yuan. Just wouldn't happen.
The US dollar is currently implicitly backed by oil. We 'print' (not literally - that's not how money is created) immense amounts of money to pay for things we cannot afford which ought have a catastrophic impact on any currency. We create 'growth' in wealth by dumping aforementioned funny money into assets creating price inflation -- quantitative easing. And our deficit is gradually growing out of control meaning we're left ever more paying off old debts by taking on more debts -- a policy that has a special term in the world of finance...
But the big thing here is that oil is still by far the most in demand resource in the world. And, thanks to some incredibly prescient negotiations dating back to the 70s, the majority of all oil producing nations only settle oil contracts in the dollar. This means that if you have a dollar you have access to oil. This creates an amazing system of externalizing stability. Imagine the value of the dollar decreases. This incentivizes foreign nations to increase their reserves of the dollar to ensure stable access to a fixed amount of oil. This, simultaneously, creates a natural dampening affect on any sort of inflation as that money is taken out of circulation. And this even applies with the Mideastern nations themselves. Saudi Arabia and other nations also agreed to purchase US securities with whatever leftover dollars they have after accounting for national expenses. Once again, helping to mitigate any negative consequence of let's say 'creative' economic policy.
Oil, the petro dollar in particular, stabilizes our currency and our economy. If you take the control of oil away from America, I do not think our military might alone would be sufficient to keep the dollar stable. And if the dollar loses stability our entire nation implodes. Everything that happens in the Mideast is based around this relatively simple fundamental aspect. Iran, Iraq, Syria, Libya. What they all actually have in common is that they expressed real intents to move away from the petro dollar. Venezuela has done the same.
The reason China/Russia would side against the US has nothing to do with oil or Saudi Arabia or Iran. It has to do with the US. If the petro dollar collapses, which it arguably already is, the US isn't far behind. And the US is still the greatest immediate danger to those nations. And the only reason Saudi Arabia would ever turn away from the petro dollar is if they believe the US will not be able to force them back to it, which would all but require the collapse of the US.
This whole relationship makes all the Rumors of the Sauds swapping to the yuan all the more intriguing. If that ever did happen our response could well trigger something like a worldwide Cold War. China and probably Russia would likely have an obligation of support for Saudi Arabia, America would pull in NATO and the world would likely split along one side or the other. For that matter Saudi Arabia is also not like Iran, Iraq, Syria, Libya, ... . Saudi Arabia itself is now world's third largest spender on defense in raw dollars - and #1 in the world by percent of GDP. 10% of their entire GDP goes to defense. By contrast, we spend about 3%. On top of that Mecca and Medina reside within Saudi Arabia. Propaganda would be strongly on the side of the Saudis who would portray an attack on them as an attack on Islam.