If your state is a "right to work" state, and I think it is, he can be fired, ADA or not, for repeated breach of conduct code (racist remarks, shit stains), if they even want to bother to give a reason at all.
At my last restaurant, we had to fire a pastry chef because he sometimes got shit-faced drunk on the job. He tried to challenge the dismissal citing ADA (which covers alcoholism and drug addictions, to a minor extent) with the state labor board. He failed. A stumbling drunk person with a terrible temper cannot be allowed to work in a kitchen that has knives, meat grinders, open flame grills, and raw food. Public safety trumps drunk bastard. Public safety plus civil rights to not be harassed about your race trumps mentally challenged guy's clueless antics.