In all these conflicts, individuals from both sides can read similar history books and even have the same facts taught to them, yet it is very unusual to find individuals who would agree about who started the conflict, who is to blame, who should make the next concession, etc.

In my experience, who started the conflict, who is to blame, etc. is explicitly taught as fact to each side's children. Israelis and Palestinians don't agree on facts at all. A civilized discussion of politics generally requires agreeing not to discuss most past facts.