Original post by viddy9The situation is, of course, more nuanced than MatureStudent would have you believe, with his black-and-white view of the world.
* Israel has, broadly, been supported by governments in the West, particularly the United States. The "left" has, historically, always been more willing to challenge claims made by its government: in Russia, you'll find "left-wingers" challenging the claims made by Putin to justify his interventions; in Britain, you'll find them challenging the claims made by the British government to justify their actions.
This, for a start, would invariably lead people on the "left" in the West to be more likely to find something wrong with their government's reasoning, and so be more sympathetic towards Palestine.
* The right has, historically, been less willing to challenge claims made by its government; they're more likely to believe that the government has benign, angellic motives and that their government is exceptional in some way. In Russia, right-wingers will tend to view Putin's interventions in Ukraine and Syria as humanitarian; in Britain or the United States, they'll tend to view our interventions in Iraq, Libya and so on as humanitarian.
This, for a start, would invariably lead many people on the "right" in the West to be more accepting of Western foreign policy because, by definition, Western foreign policy is always motivated by humanitarianism or freedom or democracy, or any mishaps are due to a lack of planning. Thus, if our governments are selling arms to Israel and vetoing Security Council resolutions critical of Israeli actions, this must, by definition, be good.
* The "right", particularly in the United States, significantly consists of evangelical Christians, who are overwhelmingly going to be "right-wing" because Christianity is concerned with maintaining traditions, and the "right", in part, is concerned with maintaining the status quo. Many of these Christians believe that, if the Jews manage to seize all of the area of Palestine, it will bring on the Second Coming of Jesus and the Apocalypse, in accordance with their interpretation of Biblical prophecy.
* Many on the "right" believe that what is in the national interest is best. Given that Israel is a major manufacturer of military technology for Western countries, particularly the United States, they'll tend to support Israel.
* In accordance with the belief of some on the "right" that their country is exceptional, there may be a subconscious belief amongst "right-wingers" in the United States that, because Israel is a settler-colonial society like the United States, Israel must be doing something right.
* The "left" may view the Israel-Palestine conflict in the following terms: Israel is illegally occupying, seizing and annexing Palestinian land, and denying the Palestinians a state by doing so. In these Occupied Territories, there is clear discrimination by the Israeli government and the Israeli settlers against the Palestinians, as documented by numerous independent human rights organisations. The Palestinians are the oppressed underdog, whilst Israel is incredibly powerful, meaning that one has to be more critical of Israel.
* The "right" may view the Israel-Palestine conflict in the following terms: Israel is a bastion of freedom and democracy, and is under seige by terrorists, and therefore has to be supported in order to allow it to defend itself and freedom, justice, human rights, democracy and freedom.