Zev and No One: I don’t see any confusion; I said with brevity what Zev said more explicity: In Jewish law, one is a Jew if born of Jewish mother or properly converted, though Reform Judaism has muddied those waters a bit with its acceptance of “patrilineal descent” (actually, a misnomer, but this is not the forum to discuss that mess).
By extension, one cannot leave one’s Jewishness. The evidence for this is that in Jewish law, if one converts to another faith, one does not need to go through a conversion process to reclaim one’s Jewishness. One may have to go through a ritual bath for cleansing purposes, and an interview with rabbinic authorities to explain oneself, but one does not convert back.
A Jew who abandons Judaism is still a Jew – a Jew who is sinning, from a traditional perspective, but still a Jew nonetheless.
On this board, a Jew might claim Jewishness when talking a cultural, ethnic identity, but call him/herself an atheist in terms of religious conviction.
Jewish Buddhists have their own term: Ju-Bu’s.