You may not think it a reliable source, but it those gospels are the starting point and main source for about 1.3 billion Christians including me and the dude who wrote the song. I think that any discussion of "anti-Semitic" (anti-Jew) content of the song has to start there.

Your point may be valid in another context, but when talking about the meaning of a song sung in Christian churches by people who believe in those Gospels, I do not think it is relevant.