One of the email discussion groups I'm in went into an off-topic diversion about politics, and someone raised the following arguments against Christians participating in politics (after giving some purely secular arguments against siding with a political party):
I also prescribe to Jesus words to not be any part of this world. He didn't
participate in politics when he was on earth even though many of his
followers wanted him to. His kingdom was not of this world, so why should
mine be? It doesn't matter what country you live in or what party you
belong to, we are supposed to be Christians. We should follow Christ and
not politicians that claim to be Christians.
I think this is an unfortunate attitude. I would say not just that it's not wrong to vote, but that I as a Christian have a responsibility to vote. There's enough to suggest that Jesus' command not to be of the world doesn't mean not voting, because how you vote might just be one way of being in the world but not of it.
As for Jesus' participation in politics, I would say that the main reason for that wasn't because his kingdom isn't political. It very much is. It's just that the political aspects of the kingdom aren't present yet. He will reign in the restored universe, the new heaven and the new earth. That's clear in the Revelation. The reason he didn't seek political issues during his first coming is because the people of that time thought his rule would merely be a human political reign, and he had to go pretty far in avoiding that sort of thing so as not to give the wrong impression. He certainly talked about political issues (e.g. you should pay your taxes but also your tithe and offerings), and Paul appealed to Caesar, which was a political move (for the sake of the gospel).
We're told to submit to government as Christians. This creates a tension with the fact that we also are part of the government with our right to vote for those who represent us and to put forward (and vote for/against) inititatives. However, it also shows that we are part of the government already, and therefore we should respect and honor the leaders both now and of old who wish for us to take part in the political process. That's part of how the American governmental system works, and it's that authority that I submit to as a God-ordained institution whenever I vote. My voting is thus a part of my obedience to what Paul says in Romans 13 and what Peter says in I Peter 3.
Given the ability to vote to have godly, honest, responsible, and right-thinking people in positions of leadership, I think it's a failure of my stewardship responsibilities if I don't vote. God has put me in a position where I can help to carry out the justice he so many times sent prophets to complain that Israel's leaders weren't seeking. I believe this is a gift from God, and if I fail to exercise the abilities God has given me then I would have no recourse but to accept the removal of my freedoms when he takes those abilities away because of my wasting them.
As it is, Christians have a harder time shaping public opinion and policy, and I think part of the reason for that is that God is removing Christians' voice for having failed to use it for the last 100 years or so when Christians left the academy and public life because of the liberalization of the mainline denominations (to the point of denying basic biblical statements) and the desire to band together with other believers to continue distinctively Christian academic work. It seems to be reverting in the other direction in the short term as evangelicals have been motivated to be politically involved and to try to get back involved in the academy, but my fear is that this is merely for a time, as was the case with Josiah's revival as just a short bump up in a long downward slide (and the same for the Great Awakening earlier in our country's history). Our society is becoming completely secular to the point of biblical illiteracy in the average college student (which I have experienced firsthand as a college instructor), and the reason is because Christians isolated themselves out of fear of being influenced by the wrong ideas (something Daniel didn't dream of doing -- he learned all the astrology and idolatry along with the ancient wisdom and science of Babylon -- he just didn't break God's law and eat what the law said not to eat).