the populace of both sides are brainwashed by organized religion, and authoritarians and terrorists are using that as a cudgel to achieve their own selfish aims, and are the real poison here.
The only way to take away their power is to remove the dispute over the region.
Since you’re already proposing completely impossible fantasy solutions, why didn’t you propose e.g. deposing of those authoritarians and religious extremists who fan the fires of conflict, assembling representatives willing to work out a tolerable solution to the conflict, and thus allowing the area (especially Palestine) to gradually develop, and naturally ease and dispose of the extremist culture that most people there are born into?
No, that sounds boring, let’s just take everyone, terrorists and normal people together, and dump them into the Amazon rainforest or Tierra del fuego. Even in your fantasies you don’t seem to wish for especially nice things for those people.