The Saudis (and Iran) are among the countries calling for a nuclear weapons free zone over the Middle East; the US and Israel have a different opinion:
"Saudi Arabia is not known to have a nuclear weapons program.
"From an official and public standpoint, Saudi Arabia has been an opponent of nuclear weapons in the Middle East, having signed the Treaty on the Non-Proliferation of Nuclear Weapons, and is a member of the coalition of countries demanding a Nuclear-weapon-free zone in the Middle East."
Nuclear program of Saudi Arabia - Wikipedia
The Saudis have always opposed nuclear weapons in the region..
If Israel continues to threaten Iran, Iran will be forced to get nuclear weapons and then the Saudis will be forced to get nuclear weapons.
What the Gulf States want and need is nuclear desalination.