Believe it or not, they're not exactly a 1-to-1.
Up until fairly recently, Israel was a stand-out in the region for actually having things like decently fair elections and a political class derived from a relatively wide sample of its populace. Other countries in the region were either Arab nationalist republics, Islamic republics, or authoritarian monarchies. While it was ethno-theocratic, it was one that seemed to balance religion with secular demands, and as it is, most countries around the world have at least some basis in ethnicity. The US is a notable exception for this, for what it's worth. This has begun to fade as a more conservative sector of Israeli society has begun carrying more political power, but it's not to the same extent as you find in other countries in the region.
Nuclear weapons are indeed bad and we used to try to negotiate ways between major powers to reduce their number. We don't do that anymore, for a variety of reasons. The more of them there are in different, independent hands, the more likely they are to be used. If they're used, there's a real chance that nuclear-armed powers make severe miscalculations about who is firing what at where. For example, a USAF radar operator watching an over-the-horizon system pointed eastward sees a large number of missiles being launched, and may assume that they're Russian missiles aimed at the US, when they are in fact Iranian missiles aimed at Israel. They might make a potentially species-ending mistake as a result.
The largest issue with Iran having nuclear weapons is that it almost certainly intends to use them against an already nuclear-armed power, Israel, in a way that really doesn't have any rational endgame. Iran is a Shia Islamic theocracy. Beyond the Western-ish influence that Israel brings to the region, there are serious theological implications from the existence of Israel. Islam has a core tenant that there is no higher power other than Allah and that Muhammad is his prophet. Allah is the same god that exists in Christianity and Judaism, and Muhammad is held as carrying on the thread of prophecy that began with the biblical Adam.
There's a lot in common in the three major Abrahamic faiths, and like all other faiths, people interpret it in different ways. The Iranian regime - who definitely does not represent all Muslims, let's make that clear right now - interprets it as the basis of their power. They are a group of clerics and scholars who govern a nation through interpretation and application of religious jurisprudence via one head cleric, the Ayatollah.
If you are a person who either rules a society based on any religious jurisprudence, or are working under that person - as all of the Iranian government does - you can't have too much tolerance for things that might undermine that religion. The Iranian theocracy's interpretation of the line of prophecy that Muhammad is a part of is that he is the "seal of the prophets", meaning that there will be no further revelations or corrections to the line of prophecy until the end-times. Muhammad is held up as having revealed corrections to the line of prophecy, meaning that while Judaism, Christianity, and other Abrahamic faiths are of the same prophecy, they ultimately got some things wrong.
Now let's get back to the existence of Israel. A short description of Israel in the context of what I've described is that you have a people who now control some of the Abrahamic faiths' most holy sites, and they're doing it based off of what is seen as the "wrong" prophecy.
If people who believe in the "wrong" prophecy are firmly in charge of the sites you consider holy, what does that say about your prophecy and your claim to power based on it? Sort of reduces its power, doesn't it? You can't have that. Something has to be done.
In the eyes of the Iranian theocracy, that "something" is funding, training, and commanding militia and military groups who are sympathetic to your understanding of prophecy and having them strike out at the theologically inconvenient people. Developing more powerful weapons to use while doing so is a natural part of this. What's more powerful than a nuclear weapon? Nothing. So you make that your ultimate goal. What they might do with it, who knows, but again, simply having more nuclear weapons in the hands of more independent actors raises the likelihood of their use with potentially catastrophic results.
The plight of the Palestinians just happens to be a convenient excuse for all of this. They're Arab and majority Sunni as opposed to the Persian and Shiite Iran. If there were a two-state solution as we spent most of the last 30 years working towards, it likely wouldn't satisfy the Iranians, which is why they don't recognize Israel at all instead of saying "we'd recognize you if you retreat to your pre-1967 borders and let the Palestinian Authority govern the West Bank and Gaza Strip."