Saudi Arabia and Israel are not "buddies". They have an understanding. They have a mutual ENEMY in Iran, and the threat that Iran poses to them both caused them to put aside any issues they may have with each other. Saudi Arabia is at the very least willing to talk to Israel, whereas Iran isn't. Iran and Israel used to have diplomatic ties but it was Iran who broke that relationship, not Israel.
Iran has made it abundantly clear that they HATE Israel, so I really don't get how you can place the failure to become buddies on Israel. The Iranian government spurs its own population to burn Israeli flags and scream "death to Israel". Gee, why do you think that Israel's government isn't so eager to talk to Iran? And that's not even taking into account all the terrorism that Israel believes Iran is funding against it, notably Hamas and Hezbollah's actions.
As for the Persian Jewish population: To their credit, Iran does dissociate their Jewish community with Israel...somewhat. They're still heavily monitored but escaped the hell most in the Arab world were subjected to. Still, "shrunken" doesn't really illustrate just how reduced that population within Iran is. It's 2-3% the size of what it used to be. Some still use the much discarded estimate of 20,000 people strong (most nowadays estimate 8,500 Jews live in Iran) but even then at best that represents less than 10% of the Jewish population remaining. The grand majority of the Persian Jewish community obviously lives outside, notably in Israel and the United States (particularly in New York and LA). Oh, and they don't have nice things to say about the current government so perhaps you can consider that too.
Now, Iran isn't so welcoming towards other religions. More so than Saudi Arabia, sure; however, not so much compared to other Arab states. Iran may allow others to practice certain other faiths...however, heaven help you if you are Muslim and try to convert to another religion. That gets you arrested, at least. And if you want to paint a picture of a tolerant Iran, DO NOT look up what they do to those of the Baha'i faith.
Edit: "Israel should be allied with Iran..." Uhm....if Iran was willing, then Israel WOULD be allied with Iran. Do you not understand how much Iran hates them? No, seriously: It's one thing to believe that Iran and Israel would make good allies, but it's an insane idea that they're not because of any Israeli actions or desires. Israel would love it if Iran would establish some sort of normal diplomatic relations with them, as they used to have. Israeli-Iranian relations were broken off by the Iranians, not the Israelis, following the Islamic Revolution in 1979.
I won't argue that Iran has more in common with Iran than Saudi Arabia, at least in certain respects (women can actually go out of the house and talk to unrelated men in both, at least) but that's a very low bar. I think Israel has more in common with most of the globe over Iran, though.