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]

Source: The Collaborative International Dictionary of English v.0.48
 

broad-minded adj
1: incapable of being shocked; "he was warmhearted, sensible and unshockable" [syn: unshockable] [ant: shockable]
2: inclined to respect views and beliefs that differ from your own; "a judge who is broad-minded but even-handed" [ant: narrow-minded]

Source: WordNet (r) 2.0