I don't think that's true though. Israel and Iran were allies prior to 1979, I don't think there is any history of Iran supporting Palestine. Iran, like Ba'athist Iraq and Nasser's Egypt posture on the Palestinian cause to influence the Arab world, they don't actually do anything for the Palestinians.
Edit: I should add that Israel was supplying Iran with arms in the Iran-Iraq war.
Iran's 'beef' is with Zionism and Zionism's religious ethnonationalist exclusivity and settler-colonial-expansion mentality & activity and not with Israel's existence as national and religious 'home' of Jews and non-Jews per se.
On a religious level, Iran accepts Israel and Judaism and Jews in Israel-Palestine and always has.
On an political level, Iran does not accept Zionism and Zionist dispossession of people from their land, be they Arab-Muslim/Christian or Jew, and never will.
There are nearly three thousand years of historical support between 'Iran' (Persia) and 'Israel-Palestine' (K'nan/Canaan/'Gaza' etc), but there is no support and there won't ever be any support for Zionism.
During 50s, Moshe Dayan destroyed an important Shia mosque and shrine - that of Imam Ali - the Mosque of the Prophet Hussein (Maqam al Nabi Hussein) in Madjal (now called Ashkelon). It was over 1,000 years old and both Sunni and Shia went there on pilgramage. Dayan destroyed this and over one hundred other Muslim shrines and mosques, as well as hundreds of Arab villages. This was comparable to destroying Bamayan statues by Taliban and an act of extreme religous intolerance. Many Israeli Jews spoke out against the destruction of the 50s including the Israeli Antiquities Department. It is regretted by many academics and professional archaeologists that such dreadful acts occurred. Destruction of religious sites is not the worst of it - lives have been destroyed and the nature/face of Israel changed forever. These acts were made in the name of Zionism and not in the name of Judaism. If amends are to be made, the rebuilding of the Maqam al Nabi Hussein in its original style would be one place to start.
Already Iran trades with Israel in some things - oil and pistachio to name two. Relationship between Iran and Israel could easier be normalised however there is an NGO element within US/Israel/Russia that supports antagonistic anti-Muslim literature and promoes Israel/Jerusalem for Christian/Jew only and these are very active and have fingers in many pies and work hard at remaining antagonistic and which some high-level lords in britain support - eg. Barnoess Cox, whom i dislike intensely as her 'good intentions' pave the way to hell for us all.