Adams (2006) sees this darker skin as contributing to a negative image:
The earliest image of Kush of which we have any historical record was a negative one. The southerners were the “inferior other” against whom ancient Egyptians chose to measure their own superiority; hence they commonly appended hieroglyphic characters to the name of Kush that have been variously translated as "miserable," "wretched," or "abominable." For Egyptians, "wretched Kush" clearly had the same symbolic meaning as had “darkest Africa” for Europeans and Americans of the Victorian era.
In contrast, Snowden (1983) sees an absence of color prejudice, noting that many Nubians entered Egypt as laborers or soldiers. They were reputed for their military prowess, particularly as archers. Nonetheless, there seems to have been at least one attempt to limit their entry into Egypt, as attested by a boundary stele on the Nubian frontier:
Southern boundary that was made in year 8 under the King of Upper and Lower Egypt Khakaure, granted life for ever and ever, in order to prevent any Negro from passing it in faring downstream or journeying (?) with a boat, (and likewise) any cattle belonging to Negroes; excepting such Negro as may come to do barter in Iken or else on an embassy. Every good thing shall be done with them, yet without suffering any boat belonging to Negroes to pass downstream by Heh for ever. (Gardiner, 1916)
This text is problematic for two reasons. First, the word ‘Negro’ is used to translate nehesy (modern translations use ‘Nubian’). Although negative connotations were attached to nehesy, they may have been purely cultural in nature—the kind of scorn that is often felt toward rival peoples. It is not clear that ancient Egyptians reacted negatively to black skin per se.
Second, the motive is equally unclear. It is tempting to see the travel ban as a sort of influx control measure, such as once existed in South Africa. Yet there may have been other reasons. Snowden (1983, p. 22) simply sees an attempt to regulate traffic on the Nile.
Contemporary writings shed little light on this question. For one thing, the corpus of ancient Egyptian literature is quite limited. We know much more about how early Christians thought and felt because they were part of a cultural tradition that copied and recopied their writings up to the present day. The same was not true for the ancient Egyptians. Their cultural tradition was forgotten and even demonized by its Christian and Muslim successors, with the result that much detective work was needed to make their surviving hieroglyphic texts once more comprehensible.
For another thing, the ancient Egyptian language, like Sumerian and other early languages, functioned largely as a memory aid for key events and transactions. Not until the advent of Homeric Greek did people have a language that could truly express their inner thoughts and feelings.
We can gain more insight into this question by studying how Nubians were treated when significant numbers of them entered Egypt as laborers. Did spatial segregation persist between them and the indigenous working class? Is there evidence of assimilation? The anthropologist K. Godde (2009) tried to find an answer by studying cemeteries at Hierakonpolis in Egypt. The cemeteries were divided into three social classes, including one for the working class (HK43). Other cemeteries appeared to contain Nubian burials. When Godde analyzed the skeletal remains, he found no evidence of Nubian burials in the working-class cemetery or Egyptian burials in the Nubian cemeteries. A certain degree of spatial segregation thus seems to have persisted throughout the lives of these individuals. As Godde (2009) notes:
This biological analysis supports the differences in archaeological data between the Nubian cemeteries and HK43 and further substantiates the idea that Nubian workers were buried in separate cemeteries from Egyptians, regardless of Egyptian social status.
References
Adams, W.Y. (2006). The Kingdom and Civilization of Kush in Northeast Africa. In J.M. Sasson (Editor in chief) Civilizations of the Ancient Near East. (Vol. 2, pp. 775-789). Hendrickson Publishers.
Gardiner, A.H. (1916). An ancient list of the fortresses of Nubia. The Journal of Egyptian Archaeology, 3, 184-192.
Godde, K. (2009) The working class at Hierakonpolis. Nubian or Egyptian? American Journal of Physical Anthropology, 138 (S48), 201, 78th Annual Meeting of the AAPA.
Snowden Jr., F.M. (1983). Before Color Prejudice. The Ancient View of Blacks. Cambridge (Mass.): Harvard University Press.