Some ask “who am I to tell others they cannot...?”
I answer that I am NOT telling others what to believe.
I ask you: what indeed is in a name? Is someone a Jew if they simply call themselves a Jew? Is someone a Christian if they simply call themselves a Christian?
Is a Moslem a Christian because the Koran speaks of Jesus? Is he a Christian if he calls himself a Christian and speaks of Christian theology and of his love of Christ and of his own special place in the Holy Church?
Is he a Christian when he then reveals to you that Allah is G-d and Mohammed is His messenger?
It is the right of any organization (or at least barring a USSC ruling) to determine its requirements of membership.
The unfortunate problem for a Jew however is that Jewishness is both a religion and an ethnicity.
So a question that needs to be asked (but maybe there is no answer) is does a Jew stop being a Jew if he embraces Jesus as the Messiah?
In the case of my three friends from Back East, they were born and raised Jewish, and their siblings and parents are still Jewish...but they found themselves eventually believing in Yeshua as Messiah.