Anti-semitism is a problem here to a certain extent. There has been historical violence against the jews in the city including a quite recent bombing of a synagogue. This is compounded by Turkey and Irael's terrible diplomatic situation and current struggle for control of the region, which has led a lot of Turks to lump "jews" and "Israelis" together and attack them for nationalistic rather than religious reasons.
i do know a lot of jews who live in the city and who experience no harassment at all. They are all open about their faith (some where the star of david as a necklace) and say that most of their neighbors and coworkers know that they are jews. They simply just avoid the more conservative areas of the city and keep a low profile in regards to the police, as their ID cards list their religion.
As a tourist, I doubt very highly if you'll experience any anti-semitism unless you are wearing a shirt with the Israeli flag on it or something.