Was Marx Jewish?

This otherwise only mildly interesting essay by Eric Hobsbawm on diaspora Jewry raises once again the issue of why Karl Marx is commonly considered to have been a Jew. My understanding is that Marx's parents converted to Christianity, and Marx was raised and educated as a Christian. Marx also expressed notoriously ignorant, prejudiced and hostile feelings towards Jews. Other than the fact that his parents were born Jewish, is there any logical reason that he is often claimed as a Jew? Did his family associate mostly with Jews, or otherwise raised him in a Jewish cultural milieu? For example, did he speak Yiddish in his parents' house? Despite his upbringing, did he consider himself to be Jewish? I'm serious about these questions.

As far as I can tell, anti-Semites like to claim Marx as a Jew because they want to blame the Jews for Communism. "Progressive" Jews also claim Marx, as a "Jewish" advocate of social justice. Also, some Jews take perhaps an odd pride in the idea that the supposed "three greatest thinkers" of modern times--Marx, Freud, and Einstein--were allegedly all Jews. And because halachah (Jewish law) doesn't recognize conversions, I suppose in that sense Marx was technically Jewish. But for all practical purposes, in the absence of other evidence, wouldn't it make sense to call a child raised in the Christian religion by Christian parents a Christian? [Edit: And wouldn't that make the adult Marx a lapsed Christian?] Not that it should really make any difference whether he was in fact Jewish or not. But I am genuinely puzzled by why otherwise careful writers would simply assert that Marx was Jewish without explanation.

UPDATE: According to the comments, Marx's mother wasn't Jewish in any sense of the word. So, really, Marx was LESS Jewish than, say, Barry Goldwater, who had a Jewish father who never converted, and who was, though raised as a Christian, was proud of the Jewish side of his family. I don't think anyone sane thought Barry Goldwater qualified as a Jew, though, so Marx clearly doesn't qualify.