It's like perceiving Godfather or Sopranos as anti-Italian.

 What each of these works do is take the pre-existing, negative stereotype, accept it -- and then subvert it:  by revealing the supposed villain as fully human, with understandable emotions and circumstances.

 I'm told Broadway's Wicked does much the same for the Wicked Witch of the West.

 If Merchant of Venice didn't include some stereotypical negative qualities attributed to Shylock, then he'd be an anomalous, exceptional example of a Jew in the view of the audience. And the play would be less effective in achieving its pro-Jewish purpose.

This isn't to say that I'm accepting a Jewish woman wrote the plays. But saying Merchant is anti-Semitic is like saying "Michael Corleone" is a hostile, negative stereotype of an Italian-American.