95% of present day Jews are of Khazarian descent and in this sense Jesus was not a Jew.
Josephus Flavius tells us that back in Jesus days most Judeans and specially those among the Pharisees and the Saduceans, that controlled the Temple, were of Edomite descent and that the only Israelites were found among the Galileans, the Essenes and the Zealots.
Jesus was a Galilean and thus an Israelite from the House of Judah.
In the times of Jesus there were not Jews, because Jews proper are followers of Judaism or the Teachings of the Elders, or of the Talmud.
In times of Jesus there were in oral form the Teachings of the Elders and the followers of these teachings were the Pharesees and the Saduceans.
It was not until 72 AC that the Pharisees gathered in Jamnia and there had decreed to codify in writing the Teachings of the Elders, known as the Talmud.
Jesus condenmed the Teaching of the Elders and in the name of these teachings it is that he was condemned to death by the Temple establishment: Pharisees and Saduceans.
So, Jesus was not a Jew neither racially, not religiously.