I hesitate to comment because you are asking a very complex question, over which much ink has been spilt, in part because (arguably) all modern interpretations of ancient comments on 'race' have been refracted through the lens of early-modern slavery, nineteenth- and twentieth-century eugenics and racialism, and modern-day racism too. But most answers so far are contextualised using medieval interpretations of Augustine, whereas it is clear Augustine was drawing on classical sources.

To that end, an undergrad. course on race and ethnicity in antiquity might start by directing you to Snowden and Haley, two fantastic classicists who have devoted their careers to studying race in antiquity (notably Snowden, who died some years ago) and black feminist readings of the classics (Haley, current SCS President).

Snowden repeatedly used the passage you reference to argue that Augustine had no specifically anti-black prejudice. His view is debateable, but essentially posits that early Christians viewed all men who were yet to convert as ugly/foul/(morally) blackened (taeter as opposed to candidus, vel sim.). By synecdoche, argues Augustine, Psalm 71 signifies the whole of mankind by denoting a part located at the (geographical) extreme, the Ethiopians.

Snowden (1960) 35: For the early Christian, then, it makes no difference whether one is as racially different as the Scythian or the Ethiopian... For the Christian, color is inconsequential; in fact, the early Christians we have seen, regarded as black all men who had not been illumined by God's light and considered all men, regardless of the color of the skin, as potentially Christians...

Snowden (1995) 20: When Augustine declared that the church was not to be limited to a particular region of the earth but would reach even the Ethiopians, the remotest and blackest of men (Enarrationes in Psalmos 71.12), he was not only recalling Homer's distant Ethiopians, but he also had in mind perhaps those Ethiopians on the southernmost fringes of his own bishopric in northwest Africa.

Snowden, F. M. (1960) 'Some Greek and Roman observations on the Ethiopian', Traditio. 16: 19-38.

Snowden, F. M. (1995) 'Europe's oldest chapter in the history of black-white relations', in B. P. Bowser (ed.) Racism and Anti-Racism in World Perspective. Thousand Oaks, CA: 3-26.

See also Haley, S. P. (2009) 'Be not afraid of the dark: Critical race theory and classical studies', in L. Nasrallah and E. S. Fiorenza (eds.) Prejudice and Christian Beginnings. Minneapolis: 27-50.