If Christians are to live a quiet life in conscientious obedience first to God and then to legal authority how in your opinion trained as it is by holy scripture and active faith does that affect their role as citizens, voters, and potential members of police and military forces?
Citizens - that one is easy. We go about our daily lives as Christ intended. Our citizenship makes little difference to this.
Voters - we vote for the party that we think will do the best job of governing the nation. I think too many people look to Nanny State to do what Jesus told us to do. It's easier to cast a vote so that Someone Else kinda-sorta-maybe does the nasty icky work of looking after the poor and the downtrodden, then do lots of virtue signalling to show that at least we supported the candidate that promised something other than we've got now. Jesus didn't tell us to vote for someone else to set up an unwieldy system that notionally tries to help others, he told us to help others. The Good Samaritan didn't vote for more public funding to go to help mugging victims, he got his hands dirty and helped the mugging victim himself.
Police - I'd say that's a matter of personal conviction. Depending on your view of the morality of the laws you would be enforcing and your view of the morality of the tools you may be expected to use to enforce the laws, you can sign up or not as your conscience guides you.
Military - much the same as police except you may have to decide whether to be a conscientious objector in the event of compulsory conscription.
As with most other matters ultimately God's laws trump man's laws but if you break man's laws you may have to face the secular consequences of that.