From a Jewish legal perspective, it seems pretty unlikely that Jesus was Jewish. It really doesn't make sense that Herod would have turned him over to the Romans otherwise. For a Jewish king to hand over a Jewish guy to be punished by gentiles makes absolutely no sense. It simply wouldn't happen. Especially when the gentile authorities send the Jewish guy to the Jewish king, thinking that the guy is a Jew. The only way that Herod sending the guy back to the Romans makes any sense is if Herod determined that the guy was not Jewish.
We do not inherit the world from our parents. We borrow it from our children.