Believing in Jesus completes a Jew. They are still looking for a Messiah, who has already come, and will come a second time.
You don’t get any more Jewish than Saul of Tarsus, who received revelation that Jesus is the Messiah, and “converted” to “Christianity”. He always remained a Jew, and wrote extensively about it in the New Testament for those interested in his experience.
There is NOTHING deceptive about what Jews for Jesus is doing, they are perfectly open and above board about their beliefs and practices.
Prior to Jesus, Judaism already had set guidance on what a Messiah *MUST* do to earn that title.
Jesus did not fulfill it.
Q.E.D.