free-thinking latitudinarian undogmatic undogmatical

from 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]