What a fascinating question! I think that the first systematic act of anti-Jewish beliefs was when Nimrod threw Abraham into the fiery furnace because Abraham refused to adapt his belief in Monotheism to Nimrod's pagan view. From that moment on there has been a continual struggle between the believers in God and His absolute Unity on the one side, and the believers of division and paganism on the other.
According to this it transpires that "anti-Judaism" was sparked off by the actions of one man and actually pre-dates the Jewish Nation by hundreds of years. Jewish Tradition teaches that the only way that we can expect anti-Semitism to end is with the Messianic Era, when we, the Jews will finally accept and acknowledge, together with all the other nations of the world, that we are God's Chosen People.
If you are interested in understanding the phenomenon further there is an excellent book on the subject called "Why the Jews? by Joseph Telushkin and Dennis Prager.
