Ok, so, what we know of Paul's theology and life comes from 3 sources (more if we count outside the Bible with Clement 1 and the anti-Marcionite polemics (Marcion was an early Christian theologian who preached that Jesus was not the son of the Hebrew God but a "higher" god and threw out the entirety of the bible except Paul and a cut down Luke-Acts.)

Basically, what we know seems to be in direct opposition to Roman policy towards Jewish political movements of the time, and while Paul lead the Gentile church, he was himself Jewish. The Romans were not interested in co-opting Jewish millennial movements, and they were even less interested in allowing them to spread to Roman subjects or citizens. They had an uncompromising attitude to the "God Botherers" who adopted Judaism to a greater or lesser extent, confiscating their property and exiling them from cities.

This gels with Paul's writings on the Roman Empire in his letters (It's evil and bad and we're gonna destroy it with the power of god, but don't bring down the hammer on us, concentrate on building the community and keeping it unified, do a Utopian Socialism if you can but don't get weird about it.) and the effects of his teachings, which were persecutions of the community (though not as much as later tradition might suggest) and at least one deadly riot put down by Roman Soldiers. Finally, of course, he was imprisoned, and probably executed, by Rome.

Luke is clearly a Pauline Christian, but is substantially more hostile to the Roman Empire than Paul's muted opposition, and to the ruling classes in general. Luke is particularly hostile to the rich upper classes in the Empire, especially rich subject peoples that it clearly views as compradors. It is on the surface saying that the Empire is compatible with Christians, who are non-violent, pay taxes, are sometimes citizens etc, but then proceeds to tear apart almost every institution.

On the other hand, it's fairly sympathetic to individual Roman officials, portraying Rome as an unjust system that even just men cannot avoid interacting with, and must do so on it's terms, but without giving ground where rights or privilege can be demanded. Nevertheless it prepares early Christians for persecution.

You might ask, "Well maybe Paul is quieting down an already violent radical movement" but then why is he focusing on maybe a thousand already semi-pacifist Christians scattered over Asia Minor and the Levant when in Judea, which he avoids like the plague, there is a violent Zealot Revolution in the works and he is already a learned member of the specific sect it comes from. Why are you sending him to a group of people who hate him when he could march in and corrupt the guy's that are about to fuck up an entire Roman Legion?!