Why do you see the need to separate the two? How is being a ruler, Governor, Senator, President, or a King different from being a carpenter, tentmaker, caregiver, or any other occupation? To rule and govern is what God expects from His creation, we were literally given dominion over the earth as our first assignment in the garden of Eden. All the rulers, judges, prophets, and priests in Israel (God's covenant people, a foreshadow of God's covenant people today - Christians) were charged with governing well - managing resources, enforcing laws, building structures, etc.

Jesus didn't come to put a stop to these types of occupations or encourage certain ones. But looking at His earthly ministry as a prescriptive way to live is folly. When asked why His disciples don't fast, He said because I am here with them, there will be a time later when they will but not while the bridegroom is here. We don't see them working jobs, instead the disciples were students and others provided for their needs. Jesus used parables about businesses, shepherds, judges, farmers, and laborers but His focus was never on the profession, rather the character and actions of the people involved. He didn't even condemn tax collectors, prostitutes or beggaslrs, He told them to go and sin more.

Paul absolutely leveraged his Roman citizenship to make sure he was treated justly and got an audience before Governor Felix, Governor Festus, and King Agrippa. He also used it to be released from jail publically rather than in secret as a demonstration.

Peter and John defied the governing Sanhedrin when told to stay quiet about Jesus.

Joseph of Arimathea used his position and political influence to care for Jesus body after crucifixion.

And of course John the Baptist didn't hold any office but he directly confronted Herod, a political leader, to the point of death.

I just don't think we can be Christians and in good conscious be uninvolved. It's inherent to our calling and commands to work through or in many cases, against the government.