Keeping in mind that Homer Barron is a construction foreman and northerner, while Emily Grierson comes from a genteel southern family, how do the descriptions and actions of these two characters support the theme of postbellum Southerners clinging tightly to their way of life and resisting modernization?

When Faulkner first introduces Homer Baron in “A Rose for Emily,” he is described as “a big, dark, ready man, with a big voice and eyes lighter than his face.” This description indicates that Baron works outdoors and has a boisterous, domineering personality.
The narrator remarks that ladies about town are appalled when Emily began hanging around Homer Baron; the ladies say, “Of course a Grierson would not think seriously of a Northerner, a day laborer.” This indicates that Southern society is very judgmental, both of Baron’s birthplace and his social status. Emily, on the other hand, is emblematic of the antebellum South where the dignity of one’s name precluded one from even considering a person like Homer Baron a worthy suitor.
This distinction is further demonstrated in the rumors that Jefferson spreads about Homer: “he liked men, and it was known that he drank with the younger men in the Elks' Club.” This quote suggests that Southerners are skeptical of the motives of Northerners who seem to overstay their welcome, as Homer appears to have done. They don’t understand why Homer is still hanging around after his contract is complete, so they infer that he must be trying to improve his social status by marrying a woman he believes is wealthy.
The townspeople go to great lengths to control Emily’s life, especially when it comes to Homer Baron. She is a relic from a time when prominent families controlled everything in the South, and although times have begun to change, the people of Jefferson still expect Emily to embody the old way.
Homer Baron, to the people of Jefferson, is a foreigner who must be prevented from commingling with an aristocratic Southern lineage. Their mistrust of him represents their mistrust of the North itself.