First of all: what I mean here by “Jew” is nationality/race and not religion. The question of whether Jesus was a Jew therefore means whether Jesus was an Israeli, i.e. a descendant of Jacob/Israel. The focus here is not on whether Jesus was a Jew from a religious point of view, i.e. whether he was a follower of Judaism.
Was Jesus a Jew at all? He had no Jewish father, he is not from Jewish sperm. According to the Bible, a child inherits the nationality from the father. Two examples: 1. The wife of Joseph was a Gentile (Egyptian), and with her he made two children, Ephraim and Manasseh. Although their mother was a Gentile, they are still called Israelis because their father was an Israeli. They inherited their father's nationality. 2. Moses allowed the men of Israel to take Gentile women, but he didn't allow them to take Gentile men for Israeli women.
Since Jesus did not come out of Jewish sperm, he can't be a Jew by nationality. It's wrong to say that Jesus was a "half-Jew" because his mother was a Jew. In the Bible, there is no such thing like "half". You are what your father is. If your father is Italian and your mother is Spanish, then you are Italian. You are not half-italian and half-spanish. You are what your father is because out of his sperm you came.
However, if someone wants to claim that the nationality goes from mother to child, then he must agree that Ephraim and Manasseh were not Israelis but Egyptians since their mother was Egyptian. He must also agree that Obed was not an Israeli but a Moabite since his mother Ruth was a Moabite. If he does not agree, then his position is hypocritical.
Since Jesus has no human father, he cannot biologically belong to any nationality. What does this mean now?