Judaism is the only faith that is both a people and a relgion. So one can enter the faith from either door. In the past however, one would have to be born to a Jewish mother to be considered a Jew.A "Jew" is a descendant of Judah, ONE of the twelve tribes.
All the early Christians were still Jews, as were the atheists and communists.
Following the common religion of the modernday Jews is not what makes you a Jew. It IS about lineage.