This is a bit from "God's Glory in Salvation through Judgment: A Biblical Theology" (I have a few comment underneath)

The Center of the Theology of the New Testament Letters:  The authors of these twenty-one letters are radically united in the proclamation of bizarre ideas.

To see this, let us engage in a bit of contrastive analysis, contemplating what these authors did not do and what their letters do not advocate.

Rome was not their kingdom, and they were not trying to make it home. They sought the city that is to come. Not one of these authors gave his life to address the systemic injustice of the Roman Empire by means of political reform. Not one of these authors went the way of Josephus and sought to cozy up to the emperor, though Paul seems to have had opportunities to seek such “influence” with some high-ranking officials. Not one of these authors did or said anything about trying to stop Rome from fighting its wars. Not one of them championed the idea that the government should take money from the rich and redistribute it equally to the poor, nor did they leave the ministry to advocate a government of greater fiscal responsibility, lowered taxes, and increased national security. Not one of these authors taught that the way to change the world is by initiating a universal, government-funded education program. Not one of these authors was out to make as much money as he possibly could. Not one of these authors embraced one of the popular philosophies of the day, nor did they seek to synthesize the message of Jesus with the spirit of their age. None of them advocated higher moral standards in society at large (outside the church), nor did they lobby for universal health care or a revised definition of marriage that would legitimate same-sex unions.  None of them seem to have cared whether anyone reading their letters would be perceived by the broader culture as hip, savvy, chic, or cool. They had a different program.

These authors believed that the decisive event in the story of the world had taken place. God loved the world by sending his Son, condemned sin in the flesh of Jesus, poured out all his wrath on Jesus at the cross, and accomplished salvation through that ultimate display of justice. God raised Jesus from the dead, and Jesus commissioned his followers to make disciples by proclaiming the good news.

How did they go about carrying out this commission? They all basically did the same thing. None appears to have sought to carry out the commission through political or educational institutions. According to the book of Acts, they simply told people, whether groups or individuals, who God is, what he had accomplished in Jesus, and what this implied for them. God accomplished salvation through judgment in Jesus, and the implication for every auditor of the message is that they would either believe and be saved or disobey (be unpersuaded by) the gospel and be judged. Through the announcement of judgment, the saved rejoiced in and glorified God. The converts, those who believed the message, were gathered into congregations, churches. Paul, Peter, and James all refer to elders who led these churches.

The authors of the letters studied in this chapter wrote what they did to form, instruct, and protect the churches. Their message is that God has glorified himself by working salvation through judgment in fulfillment of the Old Testament in the death and resurrection of Jesus. Their message is that there is a way of life that evidences belief in that message, and a way of life that does not. Their message is that God has sent the Spirit, who has given new life to those who believe; and the Spirit will keep them to the end, so that on the last day, when Christ comes to save through judgment, they will be those who glorify God for his mercy. The center of the theology of the letters of the New Testament is the glory of God in salvation through judgment.

I think where this goes sideways is the apparent false dichotomy between political activism and spreading the gospel.  Does spreading the gospel rule out being politically active?

If one of the messages of Scripture is that Christians should pursue justice, one way to do that is through the political system.

Other than that...the authors of Scripture wrote exactly what the Spirit wanted them to write.  No more, no less.