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Adjective: broad-minded  'brod'mIn-did
  1. Incapable of being shocked
    "he was warmhearted, sensible and broad-minded";
    - unshockable
  2. Inclined to respect views and beliefs that differ from your own
    "a judge who is broad-minded but even-handed"

See also: broad, catholic, free-thinking, large-minded, latitudinarian, liberal, open-minded, tolerant, undogmatic, undogmatical

Antonym: narrow-minded

Encyclopedia: Broad-minded