Righteousness is being set apart and different than the world. Often the church mostly sees righteousness in avoidance of certain actions.
Of course righteousness is avoiding sin, but it is also active. Often righteousness requires us to act. The world often has very little concern for certain issues.
True biblical righteousness requires that we act. Jesus did not simply avoid sin perfectly as his fulfillment of all righteousness. He also acted and his action completed his perfect righteousness.
The Pharisees misunderstood the law by making it fulfillable by the keeping of external states and avoidance of sin. They missed the fact that active righteousness and concern for the other is the core of righteousness.
True righteousness understands that love is more important then religious expectations when these collide. Jesus did what was right when he worked on the Sabbath to alleviate dire suffering.