2Tim.2:4 No soldier on service entangleth himself in the affairs of this life; that he may please him who enrolled him as a soldier.... 7 Consider what I say; for the Lord shall give thee understanding in all things.
In the beginning of ch.2, Paul writes Timothy a short series of four proverbial expressions (vv3-6), the second of which is listed above. Perhaps it was for space considerations or time, or because he was concerned to avoid writing in terms that could be read as politically subversive (he was a prisoner at the time, possibly a condemned man already, and his "mail" might have been read)--I interpret the above proverb as counsel to Timothy to beware getting too engaged with this-worldly concerns, including (but not limited to) politics.
Ministers of Christ are officers in another Man's government. Unlike a "rank and file" church-member, a minister is not as free to immerse himself in the ordinary fray. Such is not his (apparent) calling, though the
temptation to get into such jousting can be strong. Such engagement must necessarily take time and effort, if the task is to be done well; all which time is diverted from his primary assignment.
There are multiple levels of engagement in politics for the citizens of our territories. I'm not sure where the line is to be drawn, so far as participation goes. Ironically, the question of plebiscite (voting) is not only seldom questioned, but it is considered to be the sine qua non of "good citizenship." Perhaps it is so, but its status as a Christian duty ought always to be held in suspense until other questions have been answered--again, not just once, fifty or a hundred-fifty years ago, or the day a man turned 18yrs old and was granted franchise.
But assuming voting to be the simplest privilege that may ordinarily be done, the minister as-a-private-citizen probably doesn't violate Paul's principle if he votes. Or even if he affiliates with a political party, so as to be allowed to vote in a typical primary. But what about becoming a precinct delegate? Now the level of engagement is moving up. Is this too much? Perhaps yes, perhaps no. Probably there are too many variables to make a hard-and-fast determination. But with every step up that ladder of involvement, one is splitting his commitments.
Politics is to a significant degree about wielding power. To the extent that power (in the USA) is no longer spread out and diffused in strength at the lowest level, but is concentrated in capitals both State and National, the minister is doubly at risk (in my opinion) as he is attracted toward such centers where he can "help make important decisions." There was a time when local concerns dominated politics. But now the goal is to attain one of those limited seats at the table where so much money and power has been concentrated, so that a small group of people far away from most localities make all the important decisions--choices that force everyone into the bureaucratic straightjacket, if they would like some of their money back, or just stay out of court, or jail.
This is nothing less than the formation of the Beast. Ministers of Jesus Christ need to think clearly about how their marching orders as local-pastors likely conflict with the aims of would-be Nimrods, and where they are most likely to do the most good against the builders of modern-day Babylon. Will it be by seeking a "second benefice" among the elites, in order to effect change (the noble goal of so many who go off to the halls of power just before they bow to compromises)? Or is the minister more likely to do his greatest work in the unsung way that mothers do their work? That is, by sticking to their knitting, shaping and forming the minds of those closest to them in the spiritual ways of Christ.
Christ's ministers are forming one small generation of believers at a time, which even taken all together might not "change the world," or even their own locality very noticeably in the short term. They are not focused on forming a army that must needs dominate this passing-away-world. They are forming a host of forever-people, adding one soul at a time to the ever increasing ranks of a one-day resurrected population. A multitude that no man can number, Rev.7:9.
Rev.19:6 And I heard as it were the voice of a great multitude, and as the voice of many waters, and as the voice of mighty thunders, saying, Hallelujah: for the Lord our God, the Almighty, reigneth.
Heb.12:28 Wherefore, receiving a kingdom that cannot be shaken, let us have grace, whereby we may offer service well-pleasing to God with reverence and awe: