Israel had nuclear weapons back in 1966. They could have used them when attacked during the 6-day war (a war they almost lost). They could have used them during the following three year war of attrition. They could have used them when attacked during the Yom-Kippur War. The fact that they did not and have never used them as a negotiation tactic since acquiring them shows that Israeli nukes aren't destabilizing the region.

Israel hasn't started up wars with its neighbors since its creation (we'll set aside terrorists in Palestine for another conversation sufficing to say that's definitely not a war). Iran has gone to war with almost everyone around at some point during that same 75 year period of time with a total body count in the millions.

Finally, nukes only make sense for stability if you take religion off the table. Iranian leaders have called repeatedly, publicly, and recently for the annihilation of Israel. Don't forget that it was prophesied that things on this earth won't wrap up until there's a massive war in which the Jews are exterminated.

This is all before discussing how Iran and Saudi Arabia are carrying on a proxy power struggle between Russia and the United States.