Re Jewish ethnic identity and Judaism: Judaism is a religion, but Jewish ethnic identity is indeed traditionally traced down through the mother's bloodline. (Jewish culture is, well, culture.) Someone can be ethnically Jewish but of any religion (I'm Jewish through my mother's side myself, and also an Episcopalian). The two are usually, though not always, conjoined, so you can have converts to Judaism who are not ethnically Jewish, and people of Jewish heritage who are, say, Buddhists.