Jim Adams (The Performative Nature and Functions of Isaiah 40-55, 170) summarizes the theme of shame in Isaiah 40-55: “The verb occurs eleven times and primarily in the first section. In brief, those who will be shamed are Jacob-Israel’s opponents . . . , the worshipers and manufacturers of idol-gods . . . , and those who deny that Yahweh alone is God. . . . The ones who will not be shamed are those who ‘wait’ . . . on Yahweh. . . . Further, Israel and Zion will not be shamed because Yahweh will restore his people in Jerusalem. In the light of all the above, those who put their trust in idol-gods and not in Yahweh will experience the ultimate divine betrayal and thereby shame. In contrast, the speakers here are confident that they will not be shamed because Yahweh, unlike idols, is truly divine.”
Assume Paul knew this, and then read Romans 1:16 again. “I am not ashamed” means “I am among those who wait on Yahweh, among those who share in the restoration of Israel, one of those who worships the living God.” By contrast, it means he is not an idolater and that he does not deny the God of His fathers. There is likely a polemical thrust here as well, as Paul goes on to remind Jews of their history of idolatry and betrayal. Paul, the apostle of the One shamed on the cross, is delivered from shame, and his opponents, who claim to be worshipers of Yahweh while denying the Son, will be disgraced.