While "the Church" as such (meaning as a distinct entity from the state) should never have the power of the sword, that doesn't mean (nor should it) that it is altogether banned from the political sphere.
To the contrary, the Christians who make up what is known as the church (and consequently who also are many of those governed by the state) have very good reasons to be involved in their local, state, and national politics, to the degree that they're able.(1) That is to say, Christians have the responsibility and privilege (again, to the degree that they're able) to do whatever they can to influence (through humble, rational persuasion, not through coercion) the public governmental policies (politics).
Otherwise are Christians somehow not called:
And yet there are so many who think the Christian is somehow obligated to do all the above except where it involves politics. Never mind the fact that we're even explicitly commanded to bring our prayer life to bear on the government of society (1 Tim. 2:1-3). Is the rest of the New Testament really so unclear as to what it means to be the salt and light of the earth, to expose the works of darkness, to disciple the nations, to submit even our thought life to Christ - indeed to do all things to the glory of God - except when it pertains to our involvement in how our societies are to be governed and with what standard our governors should apply (and by which standard they themselves should be judged) when carrying out the appropriate duties in the domain of the civil magistrate? Nonsense!
We would do very well to remember Paul's instruction to Timothy:
All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, that the man of God may be competent, equipped for every good work.
Primarily to what Scripture was Paul thus far referring when he wrote this passage to Timothy? To the Old Testament Scriptures of course!
Why then should we assume that since the New Testament is not for the majority explicitly concerned with the ethical responsibility in the realm of politics that God has nothing to say on the matter? Here Paul is clearly teaching that all Scripture, including (and in context of this passage, especially) the Old Testament Scripture - all Scripture is profitable to the end that the man of God would be competent for every good work (including work in the social and civil domains).
And let us not kid ourselves - the Old Testament has much to say about the ethics of government-law and policy (not just in the books of law but also in the historical books, the wisdom literature, and the major and minor prophets where we can see God's standard on how that law is to be applied), which is to say, the Scriptures to which Paul was referring have much to say about politics and the believer's responsibility in that domain.
Therefore, if Christians are to be concerned with the full-orbed Christian life, they must of necessity see that by the clear revelation of Scripture, they cannot escape the fact that there is clear revelation from God pertaining to the believer's involvement in politics.(2)
Admittedly my argument above was from a normative perspective. But the argument that Christians cannot escape addressing the realm of politics has a situational perspective as well.
It's simply impossible to live in this world without relating to it in the realm of politics. And yes, as Christians we are commanded even to submit to unjust laws such as paying taxes which we know will provide for government sanctioned abortions (so long as we're able to provide for our families in a morally upright manner (1 Tim. 5:8) and are able personally to preach and obey the gospel (Acts 5:29)).
But at the same time, we are never prohibited from doing all that we can to influence the laws of the land and the lawmakers of the land toward God's just standards, or to call government officials out when they're violating His standards of justice. To the contrary, it seems clear that many are called for that explicit purpose (Ex. 5:1; Judg. 2:16; 1 Sam. 13:8-14; 2 Sam. 12:5-7ff; 1 Kgs 13:1-2ff, 18:17-18, 21:17-19; Jer. 22:1-30, 27:1-11, 37:6-10; Esther 4:12-17; Matt. 14:3-4; Acts 4:19).
But even so, regardless of the believer's acknowledged understanding of how politics is an important aspect of the Christian life, as long as he lives in this world he is and will be faced with political ramifications daily. And so as a creature of God living in this world it is practically impossible for him to escape the political realm.
What are the options then, on a practical level (on a situational level)?
The believer can either try to ignore the political sphere as something with which God is not interested (which seems clearly contradicted by the above), or he can do his part - whatever that may be (2) - to engage the culture by being the salt of the earth and the light of the world, exposing the unfruitful works of darkness, discipling the nations, submitting all his thought life (including his thought life regarding politics) to the Lordship of Christ, and doing all things (even in the realm of politics with which he is engaged) to the glory of God.
How does that work then? Is every Christian called to engage in political activism? Surely not, no more than every Christian is called to be a missionary. But it does mean that when facing the situation of the world the Christian needs to have a Biblical, Christ-centered ethic for how things ought to be according to God's Word. And he must therefore be able and willing to think through the political issues from a Biblical standpoint. This does not mean every believer must engage in political activism. But it does mean, even from a practical standpoint, every believer needs to know to some degree how God expects the nations to be governed (or in other words, how God expects the politics of the nations to operate).
How is this achieved? Like everything else in the Christian life:
Sanctify them in the truth; your word is truth. - Jn. 17:17
In order for a believer to have an answer for the world, in order for a believer to have even a basic understanding of how God says the nations ought to be governed, in order for a believer to be sanctified to God in his understanding of politics, he needs to know the Word of God - which is to say that he must strive to know the whole Word of God, even those parts pertaining to the realm of politics (2 Tim. 3:16-17; cf. Acts 20:27).
Either way, from both a normative perspective and a situational perspective, the Church (which is to say, the individual members of Christ's body, being ambassadors of God on earth) cannot escape politics in this world.
(1) I say to the degree that they're able because some nations (like even in the Roman empire when the New Testament was being written), Christians (and sometimes the majority of citizens) are given little ability to have any say at all in the government law order. This doesn't mean that they shouldn't try. But it does mean they need to exercise wisdom in choosing their battles and knowing when and when not to speak up for their rights (Prv. 22:3).
(2) I am not here advocating that every Christian is called to engage in political activism. Further down in the article you'll see I mean simply to say:
"Is every Christian called to engage in political activism? Surely not, no more than every Christian is called to be a missionary. But it does mean that when facing the situation of the world the Christian needs to have a Biblical, Christ-centered ethic for how things ought to be according to God's Word. And he must therefore be able and willing to think through the political issues from a Biblical standpoint. This does not mean every believer must engage in political activism. But it does mean, even from a practical standpoint, every believer needs to know to some degree how God expects the nations to be governed (or in other words, how God expects the politics of the nations to operate)."
For more on the Christian privilege and responsibility in Christian activism, I highly recommend the following article by Dr. John Frame:
In Defense of Christian Activism vs. Michael Horton and Meredith Kline