Ah yes, that famous "joke" which evolves a Nazi salute after antisemitic phrases are said. I think Israel is undermining the Jewish cause with their current label-everything-we-dont-like-as-antisemitic rhetoric. But this "joke" is probably where the line should be drawn for actual antisemitic behaviour.
Whether the person was an antisemite or not, just don't go there. There is no reason to. As a joke between you and your girlfriend, maybe. But not broadcasting it to the whole world on Youtube.