I'll have to respectfully disagree. Although Turkey's racism is certainly less than many western countries, it certainly exists. Darker-skinned travellers report harassment and suspicion, as well as being called "Zenci" which is the Turkish equivalent of the n-word, or indeed the same word in English.
In less confronting ways, those that don't look stereotypically "Turkish" will find themselves hassled in a multitude of languages in touristy areas - perhaps not racism per se, but certainly motivated by the assumption that they are obvious foreigners.
Those of Kurdish, Armenian, Greek or the like heritage may find it best to avoid speaking about their background. The chance of violence is basically nil, but lectures and suspicious glances would not be a big surprise.
With those caveats, most travelers should have no problems in the city, and more likely than not, will not notice any racism, especially when compared to the west or similarly sized cities.