Ten times, the expression 'righteousness of God' is used in the New Testament scriptures. Never once is the collocation 'righteousness of Christ' ever found.
The idea of 'active and passive obedience' was introduced by Dr Owen into the Savoy Declaration in 1658. It is not present in the Westminster Confession of 1647.
Luther never mentions it, nor Calvin.
It is a legal concept, the idea that 'Jesus kept the law' and that, somehow (never expressed in scripture) this is 'transferable'.
It is absent from Romans and Galatians which is where Paul would have expounded it, did it exist. Which it doesn't.
Some attempt to squeeze it into various texts like Romans 5:18 where the correct translation reads 'by one righteousness' (the special word for 'righteousness' in this place conveying 'the execution of judgment' and referring to God's righteousness who exacted righteousness upon his own Son at Golgotha) and 2 Peter 1:1 where righteousness is a matter of justification by faith, not legal works.
But these very attempts, by their clumsiness, more attest to the truth of the righteousness of God being a divine matter (not a legal matter) than they support their own theory.
The theory detracts from justification by faith which, in scripture, is a matter of God seeing his own righteousness in the faith of the believer (Abraham believed God) and rightly evaluating (logizomai) that to the believer.
And Abraham believed God and there was evaluated to him unto righteousness : is the exact wording which is extremely precise in the several places it appears.
It is a matter of God's rightness. It is not a matter of law at all. God is righteous because he is whom he is and he is what he is (I am that I am).
If law be greater than God, and if God keep the law to be righteous then Law is to be worshipped. Which breaks the second commandment of the law.
And any scheme of 'righteousness' which is based on a legal righteousness detracts from the 'righteousness of God' which is what we find in holy scripture : ten times over.
Humanity was forbidden by God to address itself to the knowledge of good and evil in the garden of Eden. Doing so was catastrophic and led to death. It was sin to do so.
That some suggest Jesus Christ should, in humanity, do what was forbidden to humanity in the beginning just reveals how little they truly understand what the tree of the knowledge of good and evil really is.
The tree of life was that which was in the midst of the garden. Not the knowledge of good and evil. And the word of God, the word of life, was that which, in the midst, spoke truth and testified to the true nature (and source) of rightness.