They don't submit to God's righteousness because they don't understand his righteousness, and they try to establish their own righteousness.
Christ is the goal of the Law, which leads to righteousness for all who have faith in God.
Moses writes about the righteousness that comes from the Law: The person who does these things will live by them.
References for Romans 10:5
But the righteousness that comes from faith talks like this: Don't say in your heart, "Who will go up into heaven?" (that is, to bring Christ down)
References for Romans 10:6
or "Who will go down into the region below?" (that is, to bring Christ up from the dead).
References for Romans 10:7
But what does it say? The word is near you, in your mouth and in your heart (that is, the message of faith that we preach).
References for Romans 10:8
Because if you confess with your mouth "Jesus is Lord" and in your heart you have faith that God raised him from the dead, you will be saved.
Trusting with the heart leads to righteousness, and confessing with the mouth leads to salvation.
The scripture says, All who have faith in him won't be put to shame.
References for Romans 10:11
There is no distinction between Jew and Greek, because the same Lord is Lord of all, who gives richly to all who call on him.
All who call on the Lord's name will be saved.
References for Romans 10:13