I think it's much simpler than this: these are both places where there have been decades of militarized border disputes, with both sides holding some of the disputed land and significant political blocs on both sides deadly opposed to formally conceding the land they don't control.

A lot of the world's major long enduring conflicts have been like this: Russia's conflict in Georgia will heat up every few years until Georgia gives up Abhkazia and Ossetia or Russia does, Russia's new one in Ukraine will too surely for the next few decades unless there's a new border agreement, Nagarno-Karabakh between Armenian and Azerbaijan will probably remain as intractable for the next two decades as it has for the last two decades, look at the fights in the South China Sea over tiny islands that flare up every few years. Don't forget China has periodic tensions with India, too, over their disputed border with India. The biggest similarity between Kashmir and Palestine (and difference from the other conflicts mentioned) is that these places are densely populated and to some degree ethnically mixed. Karabakh, for example, was pretty much completely cleansed of Azeris, and the old Armenian community in Baku--which had been there for centuries--is completely gone.

I think you're overemphasizing the hardline Muslim aspects of conflict--they're definitely there, but they're reciprocated to some degree by hardline Jewish nationalists (I'd say Dati-Leumis but I've met a lot of hilonim who feel the same; I'd say settlers but they obviously have support on both sides of the 67 borders) and Hindutva people, respectively, who also have no interest in compromise or giving upland.

Once these sort of border disputes reach an agreement where both sides formally renounce all claims to the others land, these disputes can calm down (even if some hardline groups try to keep fighting, so long as the state doesn't let those groups act as spoilers). Look at Turkey and Greece--they fought a century of war before 1923, but once they got final borders they still hated each other but just stopped fighting (they fought again over a territority dispute in Cyprus in the 70's but that's again a different conflict over a different border). Romania and Hungary have given up fighting (Hungary makes no claims to the land of the huge Hungarian minority in Romania) and often still hate each other, but there's not really a chance of war. The many of the inter-state wars in Southeast Asia (Vietnam taking Cambodia, China taking Vietnam, etc) and several wars in the Middle East (Iraq attacking Iran, Iraq attacking Kuwait) proved to be one-offs because the state's didn't pursue border changes after the war.

I think their parallels has a lot more to do with the structure of the border disputes than anything else.