Personally, I don't care much about either Israel or Palestine as such. And frankly, unless you've got direct family ties to Israel or Palestine, neither should you. It's a minor conflict between two small people who are relatively privileged, in a region where much more serious things happen at a grander scale: compare to the massive civil war in Syria, and be worried about the progress of radical islamists in Egypt, Libya, Tunisia, Algeria, Morocco, Turkey, Lebanon, Jordan, Iraq, Iran, Pakistan, etc. It should be a tiny blip on anyone's radar, if at all, and people for whom that's not the case are visibly deranged.
Yet we're witnessing large-scale derangement around these events, and that itself is much more of a source of concern than the events. This derangement bodes a lot of bloodletting to come, and the little we can do online is to fight this derangement — for don't delude yourself into believing you can do anything about this conflict itself by protesting or cheering either online or in the streets. I don't care about Israel or its enemies (so far as I can tell, Israel and its enemies already take good care of themselves), and have little sympathy for States and military organizations in general. But I do care about this general world-wide derangement, and I'm sad whenever I see friends become victims of the syndrome one way or the other.
For instance, according to previously friendly online acquaintance Brad Spangler, an active left-leaning free-market anarchist, my refusal to unilaterally denounce Israel in its current conflict and instead my deriding those who do it with such passion, imply that I'm in the pay of the Mossad, and that I'm a criminal whom he vows to horrible torments and meanwhile blocks from his account (which prevents my giving a documented account of all the insults and absurd accusations he hurled at me). Though he is usually a strong proponent of freedom of opinion, the possibility that I might just be wrong, and that wrongful opinions may be held without making one a criminal suddenly seem alien to him. He becomes totally irrational over some absurd conflict that shouldn't even register on the scale of relevance, and in which he possesses no stake.
Just across the Syrian border, a hundred times more people are dying, but there's no indignation whatsoever from Brad or much anyone else against either of the mass-murderous belligerent parties. If we are to somehow care for the people of Palestine, the local tyrants year after year kill more Palestinians than Israel does, their local State being a greater direct enemy to the Palestinians than Israel; you'd think that of all people, Brad, as an anarchist, should be tickled by this; but no, the de facto Palestinian States do not even deserve one bit of criticism according to him or to any of the people who claim to love Palestinians. Whether you care for the actual non-combating civilians or the militants all too often accounted among "civilian" casualties by anti-Israel groups, you'll find that Hamas and Fatah kill more people than Israel, in their internecine wars, and in their systematic murder of Christians who speak up to Islamic dominance, women who speak up to rape, homosexuals who are outed, or anyone who would fail to profess enough hate towards Israel. You'd think that left-leaning people would care about freedom of opinion, of religion, of sexual behavior, and about the treatment of minorities; but you'd be wrong, these are secondary concerns: the color of the flag on a neighboring territory is more important than the actual fate of people in that territory.
More one-sided arguments abound, and I will excerpt a few more from Brad's Facebook activities. Suddenly, US aid to Israel becomes a big thing and the cause of the conflict with the US government being painted as obedient puppets of Israel, but US or European subsidies to Palestinian Arabs and to all surrounding Arab regimes, which combined top the previous, somehow do not count; unfailing support to the State of Israel is a sign of US partiality, but unfailing support to all its mortal enemies is not. A more balanced analysis might conclude that the Establishment always supports the status quo that confirms its power; that politicians have to spend money on everyone to buy their votes, then can never stop spending or lose the votes to the other politicians, all the while benefiting from the money spigot through corruption and kickbacks. But people who rail one way or the other only care for one-sided accounting. The evil genocidal rants of an Israeli politico who represents a powerless minority are inflated, whereas the systematic everyday genocidal evil of the majority party in power in the Arab region is ignored. Popular support in Israel for this action in particular are denounced as Israelis desiring war rather than peace in general, whereas Palestinians teaching their kids from the earliest age to glorify genocide and suicide bombing is ignored, and the Palestinians are presented as peace-loving victims. Israel is presented as an Apartheid State even though its minority Arabs have full citizenship, including voting rights, elected representatives and freedom of religion, whereas in Arab and other Islamic countries, Jews were expelled, Christians are oppressed, atheism is a capital offense, and you'd better not be yellow, white or black.
The Israeli military are reproached their very strength and efficiency, and the Palestinian militants are alternatively celebrated for their weakness and inefficacy or made apologies based on it. Strength becomes a vice, weakness a virtue; the least mistakes of the strong, criminal as they indeed often are, are presented as deliberate and unforgivable; but the indeed deliberate systematic targeting of innocents by the weak, criminal to a much higher degree, is presented as normal and justified. Civilization is condemned as such, while barbarity is praised in itself.
It's all a bizarre world of one-sided blindness and reversal of the most basic values. Blindness certainly is present on both sides and irks me just as much when the culprit is pro-Israel. But the reversal of values is not symmetrical. Moreover, the massive propaganda machine of the left, that notably controls most of the Western intelligentsia and all of France, is completely on that anti-Israel side. Which is why its elaborate manipulations are more in need of being addressed, whereas the trivial manipulations on the other side are more transparent and find little support, thanks to that same propaganda machine.
Note that I'm not going to argue the valid arguments on either or both sides of the conflict, neither am I going to discuss potential solutions and non-solutions — that would be a completely different discussion. My entire point here is to make you realize how the vast majority of the arguments used are invalid. They are attempts to lure and maintain the listener into irrational beliefs and irrational behavior, seeking absurd non-solutions.
Please don't take sides without learning more about the issues. But more importantly, please realize you don't have to take sides, and therefore you don't have to learn about the issues. The most important skill you should acquire is the ability to resist the pressure and intimidation to take side. Massive propaganda is used to incite you to take side, both ways. However those who are trying to manipulate you are not your friends, or the friends of anyone but themselves (if even); they are not inciting you to take actions that are useful to yourself, or to anyone involved; and they are certainly not inciting you or anyone to beliefs or actions conducive to long-lasting peace there or anywhere.
Please stop caring. Morally, indifference is vastly superior to selective indignation that you get manipulated into. And it's also vastly healthier than letting yourself manipulated: every time you're caring for something you shouldn't care about, you're not caring about something you should.