Thanks for all the quick responses. Still would like clarification on this one. Can I lower my loyalty in other cities without it hurting my main city?
Every time you gain Love for a city (Your overall City Loyalty is a combination of Love, Hate, and Neutrality), whether it be from arresting, donating, or killing Champ Spawn mobs a little bit of Love from other Cities (if you have it) is converted to Neutrality.
If you kill raiders (The red mobs) outside of a City a little bit of Hate from every City will be converted to Neutrality.
So to answer you question, if you focus your efforts entirely on one City, eventually you will become unknown to the others. How long depends on how much you've worked up other cities.