Jesus was borth in Bethlehem according to Christian tradition. To say that makes him Palestinian is a misstatement of historical fact. It make him Judean (the provence he was born in). Palestein is a relative new political construct and has no bearing at all on what transpires 2,000 years ago.
This is apparently "Cultural appropriation" by the people involved.
It is most likely the Jesus had darker skin and dark eyes but that is not a given. Most in the middle east have those characteristics.