Hi Emma! I agree with you that a lot of division comes from differing understandings of history (often propagandized tellings of history on both sides, unfortunately). And there are indeed many similarities between how the U.S. and Israel govern themselves; but there's also one key difference: Zionism. Our nations are both Constitutional Republics in the Western tradition, but only one was founded on explicitly ethnonationalist grounds. America, of course, had major problems with brutal racism for most of its history, but the identity-neutral founding ideology of our nation established in our Constitution eventually enabled us to overcome that racism. So long as Israel maintains Zionism as its state ideology, it will be forced to continue denying civil and property rights to the Palestinians in order to maintain its status as a "Jewish state." An Israel without Zionism is conceivable, but anti-Zionism is an enormously fringe view among Israeli-Jews. If Israel wants to be treated like any other Western nation, then it should start acting like one and drop its ethnonationalism (and also begin complying with international law and cease committing war crimes).
Iran and geopolitics are beyond the scope of the essay, but what I will say is that it's absolutely clear from studying history that Zionism is the leading contributor to Israel's problems in the region, and that America's continued relationship with Israel makes our own problems in the region far-worse, not better. On that subject, I'd encourage you to read John Mearsheimer's The Israel Lobby.
I'd also really encourage you to stop looking at the Israel-Palestinian conflict through a clash of civilizations lens. There are Israeli hasbarists (propagandists) who want you to see the conflict that way because it leads Westerners to align with the Israeli side, but Palestinians and Arabs overwhelmingly see the conflict as a property dispute. Rather than narrowly align yourself with any side though, you should align yourself with values. For me, as a classical liberal, one of my most important values is the protection of property rights. Israel has brutally violated Palestinians' property rights, and anyone aligned with Western classical liberal values must demand they right that wrong. You cannot protect Western values by excusing their violation when it's a geopolitical ally doing it. You can demand that of Israel while also demanding that Arab society treat women, LGBT people, atheists, etc., more in line with classical liberal values as well.
For why property rights specifically are so fundamental to classical liberalism, read this short essay from economist and libertarian theorist Murray Rothbard: fee.org/articles/human-…