Anti-Judaism Defined: Extracting a Synthesized Definition of Anti-Judaism From Langmuir and Gaston

"Anti-Judaism I take to be a total or partial opposition to Judaism--and to Jews as adherents of it--by people who accept a competing system of beliefs and practices and consider certain genuine Judaic beliefs and practices as inferior.  Anti-Judaism, therefore, can be pagan, Christian, Communist, or what you will, but its specific character will depend on the character of the competing system...Of all forms of anti-Judaism, the Christian has been the most intense because of the intimate dependence of Christianity on Judaism," pg. 57 of "Toward a Definition of Antisemitism" by Gavin Langmuir.

"Perhaps I should make clear what I mean when I speak of antisemitism or anti-Judaism...Just as individuals can be relatively free of personal prejudice and still participate actively in a system of racism, so anti-Judaism has to do with the objective effect of the words used, whether or not the people who speak them subjectively hate Jews.  This underlines the seriousness of Ruether's point that theological anti-Judaism is the fundamental root of later cultural and political antisemtism.  (Philosemitism, in other words, is no excuse.)  If the three pillars on which Judaism stands are God, Torah, and Israel, then a fundamental attack on any of the three would be anti-Judaism..." pg. 17 Paul and the Torah by Lloyd Gaston

So if we were to use these definitions and synthesize them we'd have a definition that looks like this:

Anti-Judaism is any ideological opposition to Judaism, intentional or unintentional, that attacks any of the three pillars of Judaism:  (1) G-d; (2) Torah; (3) Israel.