Conflating temporal power with Divine authority is always a trap and a temptation that needs to be resisted.
Though I also believe that as Christians we do bear a civil obligation toward our neighbor--the vocational ministry of citizen demands from us certain moral obligations. While we cannot demand Caesar be baptized (figuratively speaking), we shouldn't tolerate injustice either. We have moral obligations toward upholding the human dignity of our neighbors. While we cannot use violence to seize control away from Caesar and make ourselves masters and lords of the State; we do have an obligation to be a voice of conscience.
It is never the Church's job to create a "Christian State", but it is always the Church's job to bear witness to Christ's Kingdom through word and action; as a people of peace, mercy, and the Gospel.
Where there is the intersection of faith and politics, faith must rule over politics--that is, Christ must always be Lord, never Caesar. Caesar is not lord. Jesus is Lord. So if Caesar demands that we forsake Christ, we must tell Caesar no. If Caesar tells us let the widow suffer, or let the hungry starve, we must say no; and care for the widow and see that the hungry are fed. This is our Christian calling within the ministry of loving our neighbors as ourselves. And when, as citizens, we do participate within the political processes, our aim should be to see an elimination of unjust laws and the procurement of just laws; our aim should be to see hungry mouths fed, the naked clothed, the stranger welcomed and not turned away for simply being different. It should not be the aim to force Caesar's baptism, as though if we erect a monument of the Decalogue in the public square it will accomplish anything except make us feel powerful and in control--rather our Christian political ministry must always be focused on the wellbeing of our neighbor, emphasizing peace, justice, and goodwill in order that our neighbor might prosper. It is not to force God's kingdom through temporal powers; but rather to bear witness to that Kingdom by exercising our vocational ministry as it pertains to loving our neighbor.