Is not Christ our example?
Should we not follow that example?
Christ was unconcerned with the political system He lived under.
He had bigger fish to multiply.
Shouldn't we?
On what basis have you concluded that "Christ was unconcerned with the political system He lived under"? Before incarnating, the Son was very concerned about and involved in politics, raising up rulers and bringing down rulers. Jesus used his right to free speech to scathingly criticised the Jewish political rulers and He tried to influence them toward behaving more justly and compassionately using the peaceful and legal means available to Him. Paul, in the Spirit, used Roman law to gain advantages over his enemies. Voting by citizens was not a peaceful and legal mechanism for influencing the quality of justice in society in Jesus' days. We can vote and multiply fish. These are not either or options.
Your claim that "Christ was unconcerned with the political system He lived under" is not something the scriptures actually says. Are you Amish?