In my opinion, Emily gets away with a lot in the town because of the culture of the antebellum South. This story is set after the Civil War, of course, but some aspects of the culture seem to remain.
I see two major aspects of antebellum culture that remain and allow Emily to get away with things.
First, there is respect for the aristocracy. The Old South was a very aristocratic places with the rich planters pretty much running their areas almost like feudal lords. I think that people still defer to Emily because of that.
Second, there is a chivalric attitude towards women. The South's attitude towards women was in keeping with old aristocratic, romantic views in which women were to be put up on a pedestal and worshipped. Because of this, it is very difficult for men to be pushy and assertive in trying to force a woman to do something.
Emily Grierson is not so much a woman as she is an institution in William Faulkner's Southern town. In the opening paragraph the narrators comment:
When Miss Emily Grierson died, our whole town went to her funeral: the men through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house, which no one save an old manservant...had seen in at least ten years....
Alive, Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the town....
That she is perceived yet as a "hereditary obligation" is evinced by Emily's not paying taxes and by her having a deputation that waited upon her to ask about her taxes some years later. And, because of her name and former social position, no one says anything about the foul and persistent order emanating from her house:
"Dammit, sir," Judge Stevens said, "will you accue a lady to her face of smelling bad?"
Even today, in small Southern towns, there is a certain protocol that is observed, especially toward ladies and gentlemen both of traditional names. For in people's minds, these old names represent the Old South, an era of a certain gentility. Symbolically for Faulkner, Miss Emily represents the Old South in conflict with the North, represented by Homer Barron. Emily is in a state of decay, trying desperately to cling to a former age; she has a pride that is "too furious to die."
At her funeral, very old men in their brushed Confederate uniforms talk of Miss Emily as though they had known her, believing that they had danced with her and even courted her. Their memories confuse time, for Emily represents for them the Old South, the old institution and way of life.