You don't have the definition of anti-Semitism quite right. Even though it's a bit of a misnomer, anti-semitism is a hatred specifically against Jews. Anti-Zionism can very easily be interpreted as the belief that one of the most savagely persecuted peoples in history do not have the right to live in peace, freedom, and security in their own country. Since Israel happens to be the only Jewish country in the world, being an "anti-Zionist" is considered anti-Semitic. If you truly believe in peace for both peoples, it's better to say that you oppose specific policies of Israel, but not the right of Israel to exist, because to my ears, that's what "Anti-Zionism" means.
Russian jets pound Islamic State in Palmyra (DPA)