Although the Arab nations have tried repeatedly to destroy Israel they are not afraid of Israel using the bomb against them. Nor can they conquer Israel because Israel has the bomb. Hence it provides an excuse to never start another war with Israel.
The Saudis and other Sunni Arab countries are terrified of a nuclear Shia Iran and would build their own bomb if Iran had one. As one might imagine, the Saudis are very supportive of Israel's efforts against Iran.
So does nuclear Pakistan.
If it were somehow easily possible to strip Pakistan of their nukes, it would be done. Once a country breaks through the nuclear line, the options for dealing with them rapidly dwindle, as we're seeing with North Korea.
Once Iran has nukes, Saudi Arabia is guaranteed to pursue their own. Then suddenly the revolutions that are so common to the middle east become globally threatening to billions of people. Just picture a powerful terrorist group - whether ISIS, Hezbollah, Hamas, etc - with suitcase nukes, it's the classic dread. Nobody else has used nukes in 70 years, for good reason. That will not remain the situation if those types of groups acquire them, they're designed to self immolate. Any of those terrorist organizations would sacrifice their entire organizations, without a second thought, to detonate such a weapon in a major Israeli city. Israel by contrast, has had nukes for decades and could destroy any given nearby country at will, and has chosen to never use them. There is zero chance Israel's enemies will behave similarly: they openly, frequently call for the genocide of Israel.
To know who are exactly are they: You may need reopen the history books for 19th century history about Muhammad bin Abd Wahhab, how his father and brother opposed him, what Ottoman's Muhammad Ali Pasha tried to do, etc. connection of the said events with Arab Revolt, T.E. Lawrence, the Saud family, Palestine, Fall of Caliphate 1924, ...Things pretty much went out of hand in Muslim world
From theological perspective (aqeedah) and approach in studying the religion, you can see how much Sunni and Salafi differs.
Probably the only reason Sunni today have diplomatic relations with Saudi Arabia because they control Makkah and Madinah.
Israel has dozens, if not hundreds, of nuclear bombs. Why should Iran not have nuclear bombs as well? The US and US industry was pushing for Iran to turn more towards nuclear production in the 1970s.
Iran also has made offers for a nuclear-free Middle East agreement - offers Israel has always rejected. What is the line - Arab and Muslim states in the Middle East are not allowed to have nuclear bombs, but Jewish ones can?
Some people might say Iran has theocratic and undemocratic elements. But the US and Israel had little problem with the Shah's lack of democracy. Also the US and England backed the conservative, fundamentalist mullahs in Iran from the 1950s to the 1970s against democratic republicans like Mossadegh. The US only turned against conservative fundamentalist mullahs in Iran at the very end of the 1970s who wanted US (and USSR) interference with Iran's internal affairs ended.