So, where did the Palestinians come from? Genetically, they're indistinguishable from Jewish persons (I read a paper about that many years ago). The primary difference appears to be religion. Did a different group repopulate during the exile? Because genetics says "no". Perhaps they escaped the roundup/exile, and remained in-situ?

Though I can see how the exile would cause different traditions/culture to evolve before they returned to Judea/Palestine. You have different traditions within the group of "Jews" even today...some people don't trim their sideburns, some literally wear bags over themselves so they don't brush up against women, etc. You can draw lots of distinctions, depending on how finely you wish to slice the groups.

Regardless, they did live in relative peace side by side until the extremists (and also white colonialists) started messing it up. Which was towards the end of the Ottoman Empire.