The term Palestine might be older than the Romans, but it applied to the area controlled by the Phillistines - a Greek sea people and it mmeans invader in Hebrew.

The Romans didn't rename the entire area Palestine until after Jesus's death, so no he was not a Palestinian Jew.

He also called a Canaanite woman a dog and said his message was specific to the Jewish people.

He also said he who lives by the sword dies by it and render unto caesar what is caesars- he did not advocate against the ruling regime.

And of course, if Joseph and Mary today would try to give birth in Bethlehem, they would be lynched by Palestinians.