Why cannot they live peacefully under Jewish law if Jews could live peacefully under Ottoman as you say? Why so aggressive and so much hatred against Jews?
First of all, I don't only think of Ottoman rule, but everything before. Byzantian empire, the Khalifates, Ottomans, so on... The rulers of the Holy Lands were rarely distinctive, in feudalism borders are very blurry.
Anyway, you have to admit that living under someone in the middle ages and living under someone today is quite a different thing. If you were lucky to have a lenient rule in medieval time, your subduction would only mean having the other guys' flying in the city and paying tax basically. The rulers I stated above couldn't really hold what is today Israel by themselves - they gave authonomy to the local rulers. Having any amount of authonomy is quite soothing, and never causes too much turmoil.
I'm not saying that Byz, Arabs, Ottomans were good by nature and that they didn't want to repress the habitants of today's Israel. I'm just saying that those inhabitants were sort of lucky to have all their respective rulers far away occupied with much greater problems. From my opinion Judea didn't have a harsh rule since the time of the Romans. I hope you get my point - nobody was quite able to subdue the local populace fully in history, so populace got away being pretty authonomous and not harassed.
However, today, with state borders being very clear, with technology that makes today's thousands of kilometres as short as thousands of metres in the middle ages, it's much, much more easier to control and repress people. At this point of my story, it doesn't matter how Palestinians are treated at the moment, all I want is to prove that comparing Muslim control of the Holy Land in the medieval times and the Jewish one today is very wrong.
So, I'm not a Palestinian nor an Israeli Jew, I don't know all they know about their hatred. I know that they both hate each other pretty equally, but there actual power decides how they treat each other. Israelis are pretty much unopposed there, and they exploit that to do a lot of harm to Palestinians, who then respond with as much violence as they can preform towards the Israelis.
I'm sure there are some very bad extremists on both sides, and that points they make against each other are at least partially valid - but that's the problem actually, the fact that both sides have at least some real reason to harm each other.
However, there's no good or bad side in this one. There's only extremists from one side attacking the other, and other responding even more violently. The bad thing is that when, for example, Palestinian extremists attack Israel, Israeli people consider all Palestinians as such and vice versa. That circle goes on and on with their mutual hatreds only growing deeper and their wishes to destroy each other more real. More of the normal people become extremists, more innocents are harmed...
Who started it all? Was it one side, or were both of them simultaniously? I really can't say. I think that the very fact that Arabs had to let some new Jewish inhabitants move in and make a state after WW2 was what sparked the Arab hatred for the Jews. But then again, Jews, scared by the Holocaust were right to fear and retaliate swiftly against any anti-semitism - the WW2 was too recent to allow the same thing again. And then, Arab intolerance and hatred for the newcomers, and Jewish fear of the next Holocaust pretty much started it all. The conflict has amplified ever since and the hatred will only grow, with no real prospects of it ever ending.