According to Rabbinical law, a Jew is a person born to a Jewish mother. In a thread on Majikthise dealing with yet another race scandal around George Allen, this time involving his Jewish ancestry, which he apparently denied. This promptly degenerated into a small flamefest about the definition of a Jew.
Unlike Christianity and Islam, Judaism was never a missionary religion. It doesn’t seek to convert people. Its roots are old enough that it’s almost like a local religion, belief in which is defined exclusively by ancestry. It’s possible to convert to Judaism, but it’s a rarity, and the general definition is ethnic, not ideological.
The matrilinear definition is simply the result of rape. In the diaspora, gentile men sometimes raped Jewish women, who’d then carry any resulting fetus to term and raise the baby as a Jew. As such, it made sense to define Jewishness purely on the basis of motherhood.
None of that matters on an individual level, on the other hand. Fortunately, the days of theocracy are gone in most of the world; people are free to choose their own religions. An ethnic Jew who practices Christianity is a Christian, at least in the eyes of everyone but a few outdated rabbis and the Nazis.