Genetically, the Jews of Jesus' day were closer to modern Lebanese Christians like Hanania than to modern day Jews. A different people.
Religiously, modern Judaism is just as different from the ancient Israelite religion as Christainity is. Christians have the New Testament, Jews have the Talmud. Neither existed in Jesus's time. The modern group that closest follows ancient Israelite practice, the Karaotes, are not considered Jews by the Orthodox Rabbinate. Tells you all you need to know.