This movie appeals to people with a feminist 'sensibility'. [=this movie appeals to feminists]
The writer is remembered most for his 'sensibility'.
She's a woman of poetic/artistic 'sensibility'.
(..) which I will put out this instant... if the phallic nature of it happens to offend... your goddamned fragile sensibilities! - Does it? - No, sir. "No, sir," what? The shape doesn't bother me, sir. (..)1997 G.I. Jane