What is the Biblical basis for opposing State Brutality? If there was ever a case of a completely innocent man being beaten and killed for crimes he did not commit, it would have to be Jesus. Yet, when Peter sliced off the ear of a slave, Jesus told Peter to put back his sword ... and healed the ear of the slave.

When Paul was imprisoned and beaten 39 lashes he did not incite a riot. Instead, he sang, preached, and converted the prisoners and guards.

Thus, I must ask: from where does one get scripture support that Christians should march against police brutality; what is the biblical basis that they might do this? The case of Jesus and the Apostles in the New Testament seems to suggest otherwise.
The bible makes a case for civil disobedience when it comes to loving our neighbor as ourselves, and standing up to authorities regarding justice for the poor and oppressed, at the expense of disregarding governmental law. That's how Martin Luther King Jr. was justified in his stance on biblical, non-violent protest. 

Reference such scripture examples as: The Samaritan woman at the well; the Good Samaritan; the Persistent Widow, and others (some supporting scripture to follow below).

The bible suggests that Christians should be willing to give up our lives unto death in the pursuit of petitioning for justice for others, whether they are Christian or not. We show our love by showing, and thus teaching, God's actionable love. Isaiah 58 poses the problem of the religious showing themselves as righteous by praying and fasting, yet neglecting 'true religion', allowing fighting, instead of becoming peacemakers. Police brutality is a lack of peace; we're called to petition them for peace, in a non-violent manner, which is not to say that's the same as 'making' peace. We aren't commanded to 'keep' peace, but to 'make' it where it does not currently exist - this requires taking action in addition to prayer.

“No, this is the kind of fasting I want: Free those who are wrongly imprisoned; lighten the burden of those who work for you. Let the oppressed go free, and remove the chains that bind people. (Isaiah 58:6)

“No, this is the kind of fasting I want: Free those who are wrongly imprisoned; lighten the burden of those who work for you. Let the oppressed go free, and remove the chains that bind people. Then your salvation will come like the dawn, and your wounds will quickly heal. Your godliness will lead you forward, and the glory of the Lord will protect you from behind. Then when you call, the Lord will answer. ‘Yes, I am here,’ he will quickly reply. “Remove the heavy yoke of oppression. (Isaiah 58:6‭, ‬8‭-‬9)

Christians who do not actively work against injustice of others maintains the unjust system (an example of which is the white privilege/systemic racism in America). Someone eventually must take action for change; the bible says that's us (Christians).

"By faith these people overthrew kingdoms, ruled with justice, and received what God had promised them. They shut the mouths of lions, quenched the flames of fire, and escaped death by the edge of the sword. Their weakness was turned to strength. They became strong in battle and put whole armies to flight. Women received their loved ones back again from death. But others were tortured, refusing to turn from God in order to be set free. They placed their hope in a better life after the resurrection." (Hebrews 11:33-35)

The above found in the New Testament refers to Old Testament events, yet is summed up in the New Testament for our instructing for the present time. This is part of the 'Heroes of the Faith' chapter, and we're to take note that the heroes had active faith, rather than simply a praying/fasting/evangelistic type of faith. Unfortunately, many Christians are not willing to encounter and engage in such struggle for others (all talk, no walk when it comes to getting involved with others against authorities, like the religious who crossed the street on the Sabbath to avoid caring for a Jewish man in critical condition because it was against Sabbath law - Luke 10:30-37)

Plenty of references regarding our actions toward maintaining justice in the Bible:

Blessed are they who maintain justice . . . . (Psalm 106:3)

This is what the LORD says: Maintain justice and do what is right . . . . (Isiah 56:1)

This is what the LORD says: Do what is just and right. (Jeremiah 22:3,13-17)

Follow justice and justice alone. (Deuteronomy 16:19, 20)

For the LORD is righteous, he loves justice . . . . (Job 11:5,7)

Learn to do right. Seek justice ... (Isaiah 1:17)