The evangelists, in short, present a fairly typical portrait of Jewish interactions both in Jesus' day and in their own. All the noise, all the argument over scripture, all the fraternal name calling, is one of the most unmistakably things about the Jesus movement and about its earliest literature. Within a first-century intra-Jewish context, such arguments would and did sound like conflicting ideas about the right way to be Jewish. That way would be the way urged by the writer of the text. The gospels, when we regard them as sectarian Jewish literature, deny any legitimacy to "Israel" or as "the people of God" or of "those from above" at odds with their authors' own self understanding...I think you can reasonably say that's a constant dynamic of Jew-hatred from the 2nd century until the Danny Zamir episode of last month, and it's not going to change anytime soon. Jews argue among themselves loudly and stridently, while their haters listen in, indifferent to any context, and choose the choicest quotations with which to damn the Jews.
Do the sectarian texts of these earliest Christians promote negative stereotypes about fellow Jews? Unquestionably. But that is what Jewish sectarian texts do, and that is what polemical rhetoric does. Further, all Jewish texts, beginning with Genesis, include warts-and-all presentations of some of their Jewish characters. In this sense, the gospels are no more intrinsically "anti-Jewish" than is the Bible itself. But again like the Bible itself, the gospels, once they drifted out of their communities of origin into a wider gentile world, were read as a standing indictment and perpetual condemnation of Jews and Judaism as such, rather than as a narrative exhortation to change from the wrong kind of Judaism to the right kind of Judaism (that is, to the author's kind of Judaism). Jewish sectarian rhetoric, shorn of its native context, eventually becomes anti-Jewish rhetoric.
Though I'd note this describes a dynamic, but doesn't explain the decision to use it. The determination to hate the Jews precedes listening in to their conversations. The reason Haaretz' website is world-famous while the Irish Times' isn't, has to do with the fodder for Jew-hatred one can cherry-pick from Haaretz.