Answer 1
Unlike Christianity, which has a ritual of excommunication, there is no process by which Jews can be kicked out of Judaism. Your fellow Jews may disapprove of you, but you remain a Jew.
Answer 2
Judaism actually does have ritual excommunication called "Kherem" (חרם) or "cutting off". Two of the most famous recipients of Kherem are Baruch Spinozza and Mordecai Kaplan. It is true that no Jew, according to Judaism, can be stripped of his Jewish identity, but he can be kicked out of the community.
The act is alluded to in the following verse: Lev. 19:8 (NIV): 8 Whoever eats it [sacrificial meat over three days old] will be held responsible because they have desecrated what is holy to the Lord; they must be cut off from their people.
Even if the New Testament is accepted as verbatim recordings of history, which most historians (including leading Catholic historians) and most Jews disagree with, the trial in the Sanhedrin (Rabbinical Court) confirmed that he was a heretic, but did not go so far as to put him in Kherem. Although many of Jesus' messages were seen as blasphemies, they still recognized the unity of God and the general Jewish ethos. Spinozza was basically an Atheist, which is why he got Kherem in 17th century Holland, and Kaplan was arguing for a profoundly Deist or Agnostic form of Judaism.
Since most historians believe that there was no trial at the Sanhedrin, there would have been no time or place to excommunicate him.
Jesus was Jewish
Jesus was raised Jewish.
Jesus was born into the Jewish religion.
Jewish
Jewish, as was Jesus.
Jesus was Jewish, as were each of the Apostles :)
Jesus came from a Jewish family.
Jesus' disciples were primarily Jewish.
Jesus was Jewish and the apostles were Christians because they followed him :)
All of the apostles and Jesus were Jewish, however, they began Christianity.
When Jesus began to reform it to fit him.
it was Jesus of Nazareth.