Romans 10:3

For being ignorant of God's righteousness, and seeking to establish their own, they did not subject themselves to the righteousness of God.

God's righteousness ... as used here is not analogous to the usage of the same term elsewhere (Romans 1:17; 3:24,25, etc.), but means "God's commandments," as is the meaning in Psalms 119:172 KJV, "For all thy commandments are righteousness." The inference in this verse that Israel should have subjected themselves to God's righteousness requires that "righteousness" be understood in the sense of "commandments." This, of course, is no unusual meaning in scripture. For example, it is said of Zacharias and Elizabeth that

They were both righteous before God, walking in all the commandments and ordinances of the Lord, blameless (Luke 1:6).

In view of this, the conclusion is justified that the great failure of Israel was in the substitution of their own religious devices and commandments for those of divine origin. Some reject this, of course; but, as Ironside said,

The term, "God's righteousness," is here used somewhat differently to the general expression, "the righteousness of God."[3]

They did not subject themselves ... means that Israel had not obeyed the gospel; but their disobedience had not begun with refusing the gospel. It began when the vast majority failed to achieve any semblance of the righteousness of Zacharias and Elizabeth, a failure which was grounded in their human traditions and doctrines which they preferred to the commandments of the Lord, this being, of course, the great failing in religion today. Hundreds of churches have devised their own systems without regard to the New Testament, and frequently in opposition to its plainest teachings. Therefore, the sin of many today is the same as that of ancient Israel. Stressing their own precepts, walking in their own traditions, doing it all THEIR WAY, they simply do not obey the teachings of Jesus.

Their own righteousness ... is not a reference to Israel's seeking salvation through observance of the law of Moses, but to their reliance upon their own religious ceremonies and commandments which they had substituted for God's true commands. Such works of the Israelites were the "works of human righteousness." See under Romans 2:6.