Jesus most certainly was a Jew. He was born in the region of the world we now call Palestine (which is larger than just the Gaza Strip and the West Bank - it actually includes the modern nations of Jordan and Israel), so it technically Jesus could be said to be a Palestinian Jew.
Of course to make an equivalence between Jesus and modern Palestinian Arabs is completely historically inaccurate and intentionally dishonest. The ancestors of modern Palestinian Arabs came to the land more than 600 years after Jesus lived, during the Muslim conquest