Moreover the law entered, that the offence might abound. The text shows us that Adam transmits condemnation and unrighteousness to us, actually making us sinners. Such is not the case at all, as the context speaks of how judges make judgements, declaring some just and others wicked. This proves we have much more than a legal share in Christ's righteousness. For the Protestant, their righteousness is merely a declaration or label.
Inherent righteousness is, therefore, essential.
Acts of justice are viewed by God as right in His sight. Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city. Again and again we see how the extrinsic or declared righteousness is not in the forefront. It is nowhere to be found. Any human works would, of course, fail miserably in God's sight.