I think you are mixing things up.
Yes, Daniel did not resist getting tossed into the lion's den. But that certainly does not mean that, in the rest of his life in Babylon, Daniel was not doing his part to advocate for the God of Israel.
In other words, the fact that Daniel did not resist the lion's den is hardly an argument that we are not to challenge the powers that run our world.
The proper analogy is this: If you as a Christian are sentenced to death for advocating for the adoption of kingdom of God values in our society - something I suggest that we are Biblically mandated to do - you should arguably not "put up a fight" as you are led to the execution site.
So the Daniel example does not challenge what is otherwise clear in the Bible - Christians are indeed called to transform all the institutions of our world.
Daniel did not fight the powers that existed in his time. Daniel followed the laws of the people without protest, he did not raise a fuss about things and try to buck the system.
Daniel:6:4: Then the presidents and princes sought to find occasion against Daniel concerning the kingdom; but they could find none occasion nor fault; forasmuch as he was faithful, neither was there any error or fault found in him.
Daniel:6:5: Then said these men, We shall not find any occasion against this Daniel, except we find it against him concerning the law of his God.
Daniel:6:6: Then these presidents and princes assembled together to the king, and said thus unto him, King Darius, live for ever.
Daniel:6:7: All the presidents of the kingdom, the governors, and the princes, the counsellers, and the captains, have consulted together to establish a royal statute, and to make a firm decree, that whosoever shall ask a petition of any God or man for thirty days, save of thee, O king, he shall be cast into the den of lions.
Daniel:6:8: Now, O king, establish the decree, and sign the writing, that it be not changed, according to the law of the Medes and Persians, which altereth not.
Daniel:6:9: Wherefore king Darius signed the writing and the decree.
Daniel:6:10: Now when Daniel knew that the writing was signed, he went into his house; and his windows being open in his chamber toward Jerusalem, he kneeled upon his knees three times a day, and prayed, and gave thanks before his God, as he did aforetime.
He didn't scream about it. He simply carried on worshipping the Lord as he had always done. He did so in faith.
We are actually called to be obedient unto death if needs be.
Jesus' kingdom is not of this world.