In The Dark Knight Rises it is said that Bane was expelled from the League of Shadows. Is it known why?
There is no mention of Bane being expelled because of how he looks. From the script:
WAYNE Bane was a member of the League of Shadows? ALFRED Until he was excommunicated. And a man considered too extreme for Ra's al Ghul is not to be trifled with.
So the only thing we have to go on is that his methods were considered too extreme even for the League.
Of course later in the movie he cast's doubt on whether he really was expelled:
BANE But we are initiated, aren't we, Bruce? The League of Shadows. And you betrayed us... BATMAN Us? You were excommunicated. From a gang of psychopaths. BANE Now I am the League of Shadows, here to fulfill Ra's al Ghul's destiny...
And of course later we find he is working for Talia, Ra's al Ghul's daughter. Misdirection is one of the League's core techniques.
So in short, its not clear whether he was really expelled or not, and there is no documented reason other than 'he was too extreme'.