The charges being brought against Jesus was that he was "King of the Jews", meaning that he claimed earthly authority over the Jews. The charges, therefore, were charges against the authority of Rome.
You can see this more clearly if you read the full passage (using your source translation):
33 So Pilate entered into the governor’s palace again and called Jesus and said to himHim: “Are"Are you the king of the Jews?” 34" Jesus answered: “Is"Is it of your own originality that you say this, or did others tell you about me?” 35" Pilate answered: “I"I am not a Jew, am I? Your own nation and the chief priests delivered you up to me. What did you do?” 36" Jesus answered: “My"My kingdom is no part of this world. If my kingdom were part of this world, my attendants would have fought that I should not be delivered up to the Jews. But, as it is, my kingdom is not from this source.” 37" Therefore Pilate said to him: “Well"Well, then, are you a king?”" Jesus answered: “You"You yourself are saying that I am a king. For this I have been born, and for this I have come into the world, that I should bear witness to the truth. Everyone that is on the side of the truth listens to my voice.” 38" Pilate said to him: “What"What is truth?”"
And after saying this, he went out again to the Jews and said to them: “I"I find no fault in himHim."
When Jesus said this, he wasn't saying that his kingdom was not currently populating the Earth, but rather that he is bringing about a spiritual kingdom. He was, essentially, denying an earthly rulership that the Jews were accusing him of. He was not saying that his people should avoid politics or that they should not become rulers through appropriate means.
Therefore, there's nothing from this passage that suggests we should stay out of politics.
