The one who adopts the belief that Jesus was Christ is a Christian and not a Jew. Take a look at this:
JEWS FOR BAAL
Elijah was having a hard time. Thousands of Jews had joined the Paganism of his time and were worshiping Baal. There was something peculiar about them, though. They would insist on being identified as Jews. Perhaps they even thought they had it complete. They would call themselves Jews for Baal, and they would even have their own prophets. "The prophets of Baal."
The Jews for Baal were getting too numerous and surely, interferring with Elijah's work to promote true Judaism. This was getting in Elijah's nerves.
Then, Elijah had an idea for an experiment: They both, Elijah and the prophets of Baal would offer a sacrifice, but the fire would have to come down from heaven (skies) on the bullocks to be offered. Amazingly, the prophets of Baal were so sure of their hyphenated faith that they went along with Elijah's proposal. They were really like the faithful of Jim Jones.
If you read I Kings 18:18-39, the experiment was to define who was really God of the two, if Baal or Adonai, the God of Abraham, Isaac and Jacob. The fire from the skies proved the truth of Elijah. Our God was the only God.
And the prophets of Baal in the number of 850 of them ended their lives like the almost a thousand of the faithful of Jim Jones. These by being poinsoned to death and those by having their throats slit to death in the brook of Kishon.(I Kings 18:40)
Today we have the same phenomenon going on. "Jews-for-Jesus" and "Messianic Jews." Former Jews with the same kind of faith, who insist on being identified as Jews. The attitude is the same: They keep hopping between two opinions: The Lord our God, or Jesus. So, they follow Jesus but insist on being identified as Jews. Just like the Jews for Baal. Luky those of today that Elijah is no longer around. He would be having a hard time all over again.