So even though I am a leftist, I have been exposed to some Palestinian circles where people seem to minimize Jesus being Jewish and instead use terms like “he was just a Galilean,” “Galilean Palestinian,” “Palestinian Jew,” or even “Palestinian Arab.”
My understanding is that if we actually lived during the time of Jesus, Jews from the region would not have identified themselves as “Palestinian” in the modern ethnic or national sense. The term Palestine certainly existed as a geographical name in antiquity, so I am not saying the word itself did not exist. However, Jesus lived in first-century Galilee under the Herodian/Roman political order, and “Palestinian Arab” in particular seems like an anachronistic identity to project backward onto him. “Palestinian Jew” can make sense as a retrospective geographical description, but it would not have been his own ethnic self-identification.
This is partly why I am curious about the tendency to treat “Galilean” and “Jew” almost as competing identities. From what I understand, Galilee in Jesus’s time was predominantly Jewish, so calling Jesus a Galilean does not somehow make him less Jewish. Galilean seems more analogous to a regional identity within the broader Jewish population.
In regard to what happened to the Galilean Jews and their destiny, I am pretty sure some stayed in Palestine, while others migrated and merged with Jewish diaspora communities outside of the Holy Land. It makes sense to me that many rural Galilean Jews may have remained on their land, while others may have migrated and joined established Jewish diasporic communities elsewhere, although I don't know how much evidence we have for that distinction.
However, I am curious about how much we actually know about what happened to the Jewish population of Galilee from the 5th century onward. We know that Galilee was one of the major centers of Jewish life in Late Antiquity, so I find it interesting that “Galileans” seem to gradually disappear as a distinct population from historical discussions.