Part of the aristocracy of the Old South, Miss Emily was revered as "a monument, a tradition." Her family is one of the prominent, established ones in the community. Much as in the Edward Arlington Robinson poem "Richard Cory," the people "on the pavement," the common townspeople, simply look up to the upperclasses since wealth and social prestige is customarily something to be admired.
Some ways in which the town is respectful to Miss Emily include the town directors' resistance to directly asking that Miss Emily do something about the terrible smell that comes from her house and the respectful wait undertaken before they open the doors to the room they believed had been closed for so many years.
I think part of it is Faulkner's way of portraying (and poking fun at) the idea of old Southern hospitality. The people in Jefferson show her respect despite her many eccentric ways because she is an elder of the community.
The townspeople respected Miss Emily's father and they, in turn, respect her. Another reason they seem to respect her is partially because they feel sorry for her. When Miss Emily fails to take a hint about matters such as taxes, the townspeople would rather let it go than press the matter. Miss Emily fails to meet several town requirements such as taxes and putting up house numbers. The townspeople seem to simply let it go. They also take great care in expressing their concerns about the smells coming from her house. The men put lime around the house during the night rather than confront and possibly embarrass Miss Emily.