Possibly what would be more accurate to say is that people oppose Israel because they hate Jews and people oppose Israel because they dislike its policies. Sometimes people in the first category can look like people in the latter because they disguise their irrational hatred with rational justification. Conversely, this has made many lump those in the latter category with those in the former.
However, I think that whilst it might be technically inaccurate to equate anti-zionism with anti-semitism, it would be equivilant to arguing that "only" 5,500,000 Jews were killed in the Holocaust rather than 6 million. The focus is so off than one must question the justification for ignoring the real issue at hand.
Having said that I have seen a limited problem with regards to people using "anti-semitism" as a way of shutting down inquisitive and exploratory debate something which I can only see as increasing anti-semitism and not resolving it. But then that is a problem that is limited whereas anti-semitism itself, clearly isn't.
I have personally experienced antisemitism from both the Left and the Right and the only thing I find surprising is that anyone would find that surprising. Surely that has been the story for the whole of history?