It is important that Homer Barron is a Yankee, a northerner. Some people in the town felt that he, "a day laborer," was certainly beneath Emily Grierson socially, and some older folks "said that even grief could not cause a real lady to forget noblesse oblige." In other words, Emily enjoys a privileged status in the town, despite the fact that she does not now have much money, and they think, perhaps, that she is seeing Homer out of some sense of generosity toward him, someone who is less privileged than she.
However, after some time, public sentiment begins to change, and people feel that the relationship is "a disgrace to the town and a bad example to the young people," and they get the minister to speak with her about it. When the minister implores Emily's Alabama relatives to come, they do, and yet Emily still purchases a number of items for Homer in town. The narrators say, "We were really glad. We were glad because the two female cousins were even more Grierson than Miss Emily had ever been." So, despite their reservations about the seriousness of Emily's relationship with Homer, they begin to be glad that a marriage seems imminent because they so dislike Emily's snobbish family.
Homer, of course, represents a massive departure from the kind of man Emily's family would think appropriate. When her father was alive, "None of the young men [who courted her] were quite good enough for Miss Emily." It seems important to Emily that Homer is what the town and her family would call the wrong kind of man to marry. The narrators do reference "all the young men her father had driven away" and their knowledge that his behavior left her with "nothing." After her father rejected her suitors during his life, leaving her all alone, Emily seems a set on making a choice that her father (who condemned her to solitude) would hate, a choice of which her family (who apparently embraces the same values that he held) would disapprove, and a choice which the town (who has judged and resented her for a long time) would not like. Homer checks almost all the most offensive boxes: he's big and loud, he lacks genteel manners, he does manual labor, and, to top it all off, he's a Yankee. That fact that he's from the north would likely be one of the most upsetting aspects of his character to her family and to the father who "robbed her" of happiness.