Things that you find disagreeable or unpleasant are distasteful. A distasteful movie might disturb you so much that you leave the theater before it's over.
While certain kinds of food might be distasteful to you — overcooked vegetables, for example — you can find non-edible things just as distasteful, despite the taste within the word. This adjective uses the sense of taste that means "preference" or "tendency to like something," along with the prefix dis-, "not" or "the opposite of." You can, for example, find things like greed and cruelty to be just as distasteful as overcooked broccoli.