Art and Artist

As a lover of movies, books, art, and music, there is an idea that I think about from time to time which is can you and should you separate the art from the artist?  I think about this is for artists that I admire and those I don't admire (the artist personally not the work of the artist).  Would I appreciate Van Gogh's paintings as much if I didn't think about his mental anguish he underwent while painting?  But on the flip side, can I separate the ideals/beliefs of Richard Wagner from enjoying listening to the Ring Cycle?  When ever I see a Roman Polanski movie I think about this.  I enjoy his work as a director but I can't completely separate Polanski the director and Polanski the person. This kind of feeds into the idea that there is a thin line between genius and madness.  To what extent should we accept the madness to experience the genius?