Did you catch that? Stasis (στάσις) was a crime in the Roman world; it would get you killed. Paul is claiming they aren't wanting στάσις. But—and this is huge—the fact that he could exorcize a demon by the name of Jesus means that the claims of Jesus stand in direct contradiction to the entire pagan world system. And that especially includes the claims of Caesar to be divine.
In other words, who is God? and who demands your first allegiance? God in Jesus? or Caesar as god?
Think about that in the context of current U.S. nationalism. If I say that the U.S. is a war-mongering nation, what does that make you want to do to me?
OK, now assume that my view would destabilize not just "our troops," but the entire known world. That should give you a small picture of what he is saying here. The gospel has the potential to cause the entire known world to come crashing down.
I'm not doing a very good job of communicating this, but hopefully you can get a taste of how radical the gospel is—and how destabilizing it is to the status quo. (Mind the present tense; it's intentional!)