Is the Talmud Anti-Christian? Who Cares?

Steven Plaut asks if the Talmud is anti-Christian. He then proceeds to answer his own question in the negative (with an assist from Gil Student), by muddying the waters as to whether any of the Jesus-like characters encountered in the Talmud are actually Jesus, when they might in fact refer to Jésus, his non-union Mexican equivalent.

Alright, but leaving aside the obvious point that this doesn't really answer the question (I don't think Mein Kampf has many references to Woody Allen in it, and yet, it's probably anti-semitic), we must ask ourselves, who cares? Let's stipulate that the Talmud is anti-Jesus. Are Christians going to be pissed off? Why? Is it news to them that Jews don't like Jesus, especially the Jews they believe killed Jesus (i.e., the Jews of the Mishnaic age)? Don't they think that if we thought Jesus was all that, then we'd be Christians, too?

Besides, it's not as if the New Testament, the Christian Bible, isn't anti-Jewish. And I suspect far more Jews have come to harm from Christian anti-Semitism than Christians have been injured by Jewish anti-Christianism. So what are we so ashamed of? Maybe the Talmud doesn't like Christianity. Duh. What of it?