While not very neighborly I wonder if it is possible to enact local laws that forbid new arrivals from holding public office for say 10 years. It would not restrict their right to vote but it would give them time to acclimate to the local politics. If the newcomers find things distasteful politically, they can move or wait it out until they are eligible to hold office.
... just thinking ...
Brilliant Idea!!!! However, newcomers from Blue areas should loose right to vote in state and local elections for 5 years. Give them time to “adjust”. They would keep federal voting rights just limit state and local.