John Turturro has played some of the most authentic Jewish characters in recent cinema, from the title role in "Barton Fink" to Herb Stumpel in "Quiz Show". He has very Semitic looks, down to the curly hair and the stereotypical nose.
But John Turturro is not a Jew. He is just a very good actor.
Think about it: Turturo has also played some of the most authentic obviously-NOT-Jewish characters in recent cinema, from Pino in "Do the Right Thing" to Pete in "O Brother, Where Art Thou?" to Jesus in "The Big Lebowski". But playing Pino did not make him a bigot, just like playing Pete did not make him a redneck, just like playing Jesus did not making him a child molester.
For John Turturro is not a Jew. He is just a very good actor.