I find it slightly strange that as a composer myself, I am able to look at this question quite objectively. I know a fair number of composers including: Brian Cherney, John Rea, Jean Lesage, John Corigliano, Denys Bouliane, and most notably Bouliane's master, Ligeti. Some of these composers are VERY straight forward, logical, and seem quite "normal" with the exception that they are, for the most part, extremely intelligent. However, some of them seem to have a few loose screws. I also know a few pianists...most notably Leon Fleischer...and he seems pretty normal.
Anyway, that's my experience.