What is the biblical basis for carrying out social justice in opposition to the justice system? What is the Biblical basis for seeking social justice when such actions are considered illegal, or in opposition to the justice system?
The Bible has many examples of carrying out God's commands despite opposition from secular, or even religious authorities.

For example, Daniel and his fellow exiles were ordered not to worship God by those in authority, but continued to do so. In Acts 4, Peter and John were forbidden to preach and heal, yet continued to do so. They specifically said:


  “Which is right in God’s eyes: to listen to you, or to him? You be the
  judges! As for us, we cannot help speaking about what we have seen and
  heard.” (Acts 4:19-20)


Later in response to further orders to stop, Peter says:


  “We must obey God rather than human beings! (Acts 5:29)


In a wider context, Christians have frequently disobeyed laws that are unjust, from hiding Jews from the Nazi regime to harbouring runaway slaves in nineteenth century America.