I think many people agree that the Israeli-Palestinian conflict is exceptional - in terms of the media and public attention it attracts, as well as in terms of the passions it arouses. However it is less clear what exactly makes this conflict exceptional:
- The number of casualties in the conflict varies somewhere between 50 and 150 thousand over the whole history of the conflict (depending on whether we count only the Palestinian and Israeli deaths or add those in the Arab armies that at various points fought with Israel - see Arab-Israeli conflict.) This is less than in recent conflicts such as American-led invasion of Iraq, NATO invasion of Afghanistan, Syrian civil war, or the conflict in Ukraine - all of them incurring larger numbers of casualties in shorter time period. This is further dwarfed by war in Vietnam or the Soviet invasion of Afghanistan, where the death counts are in millions.
- Duration of the conflict is again not a decisive parameter here - Wikipedia List of ongoing armed conflicts lists many conflicts that last as long and/or incurred as many casualties as the Israeli-Palestinian conflict, but many of which are barely mentioned/known beyond the regions where they take place. History has known much longer conflicts - e.g., the French occupation of Algeria lasted about 130 years, the rivalry between France and Britain had known periods like hundred years war, etc.
- Nature of the conflict is not exceptional either - e.g., Northern Cyprus has been under Turkish occupation for half a century, and the Turkish-Kurdish conflict bears many similarities with the Palestinian struggle for independence.
- Prominence of Jews - one could argue that the conflict provides a safe way to express hatred of the Jews. Indeed, antisemitism had existed in the west for centuries, but became a taboo after Holocaust. A simple litmus test here is whether one applies even-handed standards to Palestinian and Jewish victims, and whether one denounces the abuses of Palestinian authorities against their own people as much as one denounces Israel's actions - recent incidents on the US campuses certainly speak volumes about this. However, antisemitism is largely a western phenomenon - it is unclear why it would matter, e.g., to Indians or Chinese (unless they are Muslim, in which case they may support Palestinians on religious grounds - a common misconception is that all the Palestinians are Muslims.)
Remarks:
- The answers in the suggested duplicate deal mostly with the causes of the conflict, and why the west might care about it... but it is true for many other conflicts as well - as described in this question. The answers here need to take the bulleted points into account - either by going beyond them, or demonstrating why these are particularly important in this conflict.