To set the record straight, Jesus was a Palestinian but not a Jew. He was of Arabic origin, though religiously a Hebrew, and spoke Aramaic. This also means that the Jews could not possibly have been responsible for the drama that led to the crucifixion, despite some nasty Christian accusations and scape-goating. The word Jew was coined in the 10th century to describe the European converts.Where does one start with something like this?
1. Our central source for information about Jesus is the New Testament. All four Gospels present Jesus as a Jew. Matthew 1 and Luke 3 give genealogies. He is explicitly called a Jew (by the Samaritan woman) in John 4:9. The Roman soldiers sarcastically call him "King of the Jews" in Mark 15:18 and Pilate puts a placard with the same title on the cross in 15:26. And in general, Jesus' entire environment is Jewish through and through.
2. It is difficult to figure out what Fraser means by "Palestinian." Her usage is an anachronism for Jesus' time. There were Jews (Yehudiyyim or Ioudaioi) who had been native to the area for many centuries. In Jesus' time there likely were some indigenous non-Jews like the Syrophoenician woman from the region of Tyre and Sidon mentioned in Mark 7:24-30. (Matthew calls her a "Canaanite" in 15:22.) But Jesus clearly considered her an outsider and helped her only reluctantly.
Modern Palestinians likely have some genetic connection with people like her (with lots of Arab and Crusader genes mixed in), but culturally they have virtually nothing in common with them. They speak a very different language and follow monotheistic religions (Islam and Christianity) rather than West-Semitic polytheism. I don't know of positive evidence for "Canaanites" actually in Judea in the first century (drop me a note if you do), but it's likely enough there were some. Galilee was on the border of late-"Canaanite" (Phoenician) cities and I don't doubt that a fair number lived in Galilee as well, although current evidence points to it being predominantly Jewish.
Modern Palestinians certainly have a long connection with the land, and any national identity is necessarily a cultural construct, but to call anyone in the first century a "Palestinian" in the modern sense is a big leap of logic. It is a much greater leap than calling Ioudaioi and Yehudiyyim (Yehudayyin) in the first century "Jews," since besides the long geographic presence and the genetic connection, there is a cultural and linguistic continuity and even a continuity in the use of the name (see next point). In any case, Jesus was not a "Palestinian" except in the sense that he lived in a region that was called "Palestine" (deriving and generalizing from "Philistia") quite a lot since about the second century CE.
3. The word "Jew comes" from the Hebrew word יהודי (member of the tribe of Judah) which is found in the Hebrew Bible and, once or twice, in the Dead Sea Scrolls. The earliest extrabiblical appearance of which I am aware is the Aramaic form יהודיא in the fifth century BCE Elephantine papyri (more here). The Greek Ioudaios, very common in literature of Jesus' time, including the New Testament, comes from the Hebrew. By the first century it clearly had an ethnic-religious sense over and beyond any geographical sense. The Latin Iudaeus is the source of our word "Jew."
4. I agree with Ms. Fraser that, whatever the circumstances of Jesus' death (and in my opinion we don't have much reliable information about those circumstances), Christian scapegoating of Jews over it is both wicked and idiotic. But how Jesus supposedly actually being an Arab would bear on the whole issue isn't very clear to me.
As always with these things, when I find tendentious errors in an article or book which could have been corrected with the most basic research, it doesn't make me trust the author about other things I don't know about.
UPDATE: I've added a third paragraph to #2 to clarify what I was trying to say there.
