By not supporting Zionism "in general", you mean not agreeing that Jews deserve a state of their own, which in essence is discrediting their claim to a homeland and = anti-semetic. Thats like saying anyone who does not believe that America has a right to exist is not anti-american. Of course they are Anti-American. Not supporting "things" the state of Israel does, does not constitute antisemitism, same as here where someone who is against the war in Iraq can still be pro-american, even though they may be walking on a fine line...
What about the Jews who don't support Zionism, are they anti-semetic too?