It is anti-semitic because Shakespeare lived at the end of 16 and beginning of  17 century, and anti-semitism was wide spread in England at the time. In Othello too, there are very acerbic remarks for Othello's skin colour and his African origin. Anti-semitism and racism are not modern phenomena, but have always been part of the European history.

Shakespeare's plays give full picture of Elisabethan Britain and the stereotypes that were prevalent at the time.