In our timeline in 1963, the Shah wanted to execute Ruhollah Khomeini for his opposition to the White Revolution. To prevent this, Ayatollah Shariat-Madari made Khomeini a Grand Ayatollah, a position protected from capital punishment under the Iranian Constitution. As a result, Khomeini was exiled.
in 1979, Shariat-Madari became the de facto leader of moderate clerics and everyday people who were against the Shah's regime, while Khomeini was the leader of the fundamentalist faction. Of course, Khomeini's faction won out and the Islamic Republic of Iran was born. Shariat-Madari immediately became one of the Ayatollah's harshest critics (objecting to the US embassy hostage crisis, Khomeini's system of government etc), which resulted in him being placed under house arrest. Much like the man he saved, Shariat-Madari was saved from execution by his position as a Ayatollah. He died in 1986, though the Iranian government gave him one final insult by preventing clerics from attending his funeral.
In an alternate timeline, Shariat-Madari does not give Khomeini the position of Grand Ayatollah, allowing the Shah to execute him. As a result, the religious fundamentalists in Iran are deprived of their leader. In 1979, the Shah still leaves the country, but in line with Shariat-Madari's demands, his son, Crown Prince Reza, takes over as a new constitutional monarch, with an election selecting a new secular Prime Minister.
How does this Iran fare in the world? Would it have better relations with the United States and Israel? Would it be politically stable?