No, thats not true. To walk in righteousness would be to walk according to Gods standard, which would mean we are sinless perfect. Even one sin would cause us to walk in unrighteousness.
In your eyes, there is no righteous act. Your language is absolute without examples. It does not say this behaviour is acceptable, that is not. You close the door on righteousness and say we are so lost, even in Jesus we cannot walk correctly.
So if Jesus prompts me to give a gift to a friend, that is sinful because I am doing it.
I would suggest that action is righteous because it is not a sinful act.
Now the deeper question is about my motivations. They need to be sorted through over time, but Jesus in effect says this will happen by itself as He changes me, as long as I start to do righteous acts or good works.
Now I see the cross as not just a legal payment of a debt but as the declaration of commitment of God to love and people who listen to Him. It changes the emotional equation of trust, importance, loyalty, morality, once you let it work through who you are.
But most here are so religious, they will only hear religious equations of justification, putting us right, solving the problem of guilt and not I can run up to God and say thankyou, I know you love me, what can I do to serve you?
At this point being sent out and then being called sinners in condemnation and guilt sounds wrong. No it makes sense if through this we have real victory over sin and death, and walk in righteousness, going forward to share this victory empowered by the love at work in our hearts through the cross.
And no I am not perfect or do I fully understand walking in righteousness, but I do not agree with those who say this is impossible, because that denies the obvious teaching of Jesus and the apostles.
It is obvious though it is the theology that limits the aspirations, not reality.