The Collaborative International Dictionary of English v.0.48:

broad-minded \broad-minded\ adj.
   1. incapable of being shocked. Opposite of shockable.

   Syn: unshockable.
        [WordNet 1.5]

   2. inclined to respect views and beliefs that differ from
      one's own. Opposite of narrow-minded. [Narrower terms:
      free-thinking, latitudinarian, undogmatic, undogmatical]

   Syn: broadminded, broad, liberal, tolerant, open-minded,
        open.
        [WordNet 1.5]