The petrodollar is kind of fictional and has been for like 50 years, it is kind of a fake internet conspiracy theory that oil underwrites the global financial system and the dollar’s status as global reserve currency. Protecting this fictional thing is not our reason for engagement with Saudi Arabia.
The United States is a superpower with global interests. That is a fact, it is likely to remain a fact for hundreds of years, even as other superpowers arise and we shift to more of a multipolar global world. In looking at our relationship with foreign countries we have to consider a range of factors:
For Saudi Arabia the defining motivation for our relationship with them since at least the late 1980s has been that first bullet point–regional political concerns. The United States has vested interests in the Middle East, not just because it is an important oil producing region (that’s often stated as the only reason we care about the Middle East), but because it’s just a plain important region politically, economically etc–it has been for millennia. There’s a reason so much of the history of the Middle East revolves around trade, particularly between East and West. We also have ideological political affiliation with Israel, and Israel’s position in the Middle East has historically been precarious.
Simply put, if the entire Middle East was our enemy, we would have lots of problems vis-a-vis our larger political goals in the region. So we have to have some level of “positive” relationship with some of these countries. I won’t even delve into the “Great Power” realpolitik aspects of it, but that’s all wrapped up in the broad statement that the Middle East is politically and strategically important to the United States because the Middle East is politically and strategically important. The economic importance of Saudi Arabia’s oil production is but a portion of this. Also keep in mind it’s not the aspect of our relationship with Saudi Arabia which defines why we want to be on good terms with them–for the purposes of trading oil you don’t have to be on particularly good terms. Until very recently the United States still did a lot of oil trading with Venezuela, a country we’ve been on terrible terms with for like 25 years. Aside from our crazy stance on Cuba, the United States actually has a fairly long history of trade with its outright enemies, reserving true blocking of all trade to only a small list of countries we have basically marked out for very specific and vehement enmity (North Korea, Iran, Cuba and a couple others.)
So with it resolved we have vested interests in the region, the question then becomes, “Why Saudi Arabia?” Well, Saudi Arabia is rich, relatively large, and relatively open to aligning with our strategic interests. It’s really a very similar calculation that has us in bed with Egypt to a degree, and formally allied with Turkey. Turkey has been a formal ally for many years, and that was facilitated in part because Turkey had a greater historical respect for human rights, was usually more willing to host major U.S. troop deployments (we have several permanent bases there), Turkey was also a quasi-democracy and etc. Things are going in a different direction with Turkey moving more towards pure autocracy, and shifting strategic interests away from us and toward Russia. That alone probably means our relationship with the other significant Middle Eastern powers–Egypt and Saudi Arabia, are even more important. There’s obvious arguments that Iran is important too, and that’s why we had close relationships with Iran for many years. The reality is the events of the past have happened, and you cannot erase them. The reality from those events is we are on very poor terms with Iran and nothing is going to easily fix that. That’s really the core reason trying to make it an issue of “is Iran more or less evil than Saudi Arabia and which one should we ally with” isn’t realistic. You don’t patch a relationship as terrible as the U.S.-Iranian one over night, and trying to argue about which country is more “evil” by Western standards is like splitting hairs.
I think all of this is to say Saudi Arabia’s relationship with us is such that we need to accept there are some things Saudi Arabia is going to do within and without its borders that we don’t like, and that may be contrary to our interests. But as long as the overall relationship is a net benefit, it is highly questionable to sever it. So if we aren’t going to sever it, we should try to arrange it as much as possible to our benefit. On ethical issues like the Kashoggi killing and Saudi Arabia’s horrific mistreatment of women, religious minorities etc we basically need to use soft power to try to prod KSA in the right direction without doing things that push the relationship to a breaking point. Even friends can brush other friends back for outright violations–for example Germany condemned us pretty vehemently when we got caught spying on them recently, but our strategic relationship with Germany was never at serious risk. Likewise we needed to come down hard on the Kashoggi killing, but with recognition we aren’t severing this relationship. We needed to send a message that “okay you did this, and this makes us very unhappy”, because we want KSA to understand that this relationship goes both ways–we’re going to do some things they don’t like, they’re going to do some things we don’t like, but if they push that too far with too egregiously out of bounds actions the relationship could be imperiled. I think that right now, that’s all that is really needed. Trump made some really bad moves by doing absolutely nothing to keep some of our more “troublesome” partners reigned in, and they responded accordingly.