It is absolutely possible for Jews to be anti-Semitic. In fact, whole university courses have been devoted to the subject of Jewish self-hatred.
Throughout history there have been examples of Jews internalising the negative image others have of them and becoming anti-Semitic themselves. This is precisely what occurs when Jews subscribe to anti-Zionist beliefs. They are internalising the criticism of Israel and the attacks on Jewish right to self-determination, causing an identity crisis and manifesting itself as feelings of anti-Semitism.