Trying to distinguish historically between Palestinians and Jews 2,000 years ago is a bit futile, because 2000 years ago you are basically talking about the same people. The distinction today that underlies the conflict isn't about genetics, it's about history, ownership of territory, accompanied by largely shared religious traditions that have diverged over the years which provide a marker for the two sides.

Here's an interesting piece making these points, by an English medical writer, coming to the conclusion The shared genetic heritage of Jews and Palestinians :

"Jews and Palestinian Arabs are blood brothers - although this close genetic relationship probably stems from pre-Judaic times, rather than any more recent conversion of Palestinian Jews to Islam.

And the bad news? Well, this basic story has been known for the best part of a decade now. But, perhaps unsurprisingly, it hasn't lead to the warring sides laying down their weapons and engaging in a group hug. This is a religious conflict, not a genetic one."