Otl, after the iranian revolution, the USA, under Carter gave Mohammad Reza Pahlavi, the ousted Shah, refuge. Which went over poorly with the Islamic Republic. But what if we didn't? What if we approved the revolution, at least on paper. This would keep us away from Saudi Arabia over the 20th century and would leave us less likely to help them if Saddam did anything, assuming he was still in charge after the iran-iraq war, which would certainly see America helping the Iranians.
In fact, with us in with Iran and not Saudi Arabia, after 9/11, if it's not butterflied away, i'm willing to bet we go right for mecca. and a Saudi-Arabian war would likely be far, far easier than Iraq or Afghanistan, with Arabia's flat terrain and lacking infrastructure outside of Mecca and Medina.
Or we keep out of the ME other than Israel and Turkey. that works too.
If your goal is to avoid the hostage crisis and add more flexibility for a less than hostile relationship with Iran your proposed PoD can suffice.
It does not suffice for eliminating the defense of Saudi Arabia as a major concern for the United States.
If you want to do that, you need to go back further, and not have Nasser's Arab nationalist regime and later Arab nationalist regimes in Iraq and Syria deliberately decide to be pro-Soviet, anti-American, anti-Saudi, and anti-Israeli at the same time. It was natural for some of Nasser's and Arab nationalism's targets to end up working together.
Because of its repulsive to western culture domestic behavior, and its brand of Islamic holier than-thou-ism that gets mutated by competition into terrorist justification, people are obsessed with Saudi Arabia as the villain of the Islamic world now and forever. But it wasn't always this way.
While they were backward and feudal, in the 1950s and 1960s it was the Egyptian Arab nationalists who were gassing Yemeni citizens, while the Saudis were supporting the resistance. It was Arab nationalist groups, not Muslim fundamentalists, who first did international hostage takings and terrorist bombings. The first suicide bomber in Lebanon was not a fundamentalist but from the fascist SSNP or the Druze socialist PSP. The first Muslim fundamentalists to copy those terrorist tactics pioneered in the region by nationalist and socialist leaning groups were not Saudi-supported Sunnis, but rather Iranian supported Shias. The first wave of irregular fighting organizations motivated by Sunni Islamic ideology were more standard-issue guerrilla fighters (in Afghanistan) than international terrorists.
Sunni Islamists with some theology in common with Saudi Arabia displacing secular nationalists and Shia fundamentalists as leading perps of terrorism was a phenomenon that mainly emerged in the 1990s. For example, Hamas, which was a largely a social organization which hadn't done jack shit in terms of violent resistance and suicide bombing before the Oslo Accord (or at least not before the Madrid Talks), chose to pick that shit up just at the time the PLO was putting it aside, to be spoilers. I guess they succeeded. And over the years they've mainly switched to intermittent rockets and put suicide attacks behind them.
Bin Laden, Zawahiri, Ramzi Yousef, maybe Mir Amal Kansi and people of that generation in the 1990s were the ones who shifted things to people with Salafist or Wahhabist ideology and Saudi-related backgrounds being the most frequent practitioners of terrorism in Muslim-majority countries.