It theory it should be like you said, and in fact "if you identify yourself as being Christian, but don't follow Christianity, no one in their right mind is going you say "YOUR NOT A CHRISTIAN!!"". But if your mother is Jewish, that's completely different. Whatever you say, the Jewish community will see you as Jewish. But if your father is Jewish and your mother not, then the community will kind of accept that you are not Jewish.
It theory it should be like you said, and in fact "if you identify yourself as being Christian, but don't follow Christianity, no one in their right mind is going you say "YOUR NOT A CHRISTIAN!!"". But if your mother is Jewish, that's completely different. Whatever you say, the Jewish community will see you as Jewish. But if your father is Jewish and your mother not, then the community will kind of accept that you are not Jewish.