Emily absolutely does not like change. She also avoids social situations. Both these facts are clear in her behavior:

• resisting the "new" metal numbers
• avoiding the town, even after her abusive father died
• clinging to one man always, either her father or Homer Barron
• refusing to part from the dead body of Homer Barron

Likely because her father kept her isolated, Emily does not know how to handle the ups and downs of life.

We aren't told Emily's dislikes directly, but we are told she doesn't go out any longer, and we can assume she doesn't like change. She doesn't like being left, which seems to her like being betrayed. She doesn't seem to like the new metal numbers for addresses that the post office introduces.