There is no reason to blame Beard for the controversy, unfortunately the topic of race in antiquity is controversial whenever it arises thanks to some vocal and misinformed groups. Nothing Beard said was without solid basis in existing scholarship which I want to demonstrate by addressing the role individuals we might consider "black" played in the Roman Empire.

#Was there even a significant amount of black people in the Roman Empire?

There were absolutely enough individuals that we would consider black living in and around the Roman Empire to leave an impression on the historical record, and not just archaeological remains. From the Roman poet Luxorius' description of the black athlete Olympias to mosaic art we know they were familiar enough with them. Virgil describes one such woman as a servant in Italy in Moretum

Her nationality was African, And all her figure proves her native land. Her hair was curly, thick her lips, and dark Her colour, wide was she across the chest With hanging breasts, her belly more compressed,

Although the African peoples living around the Mediterranean and northernmost regions of Africa were more similar in appearance to Near Easterners, there were also darker ethnic groups mostly originating in the Saharan region and migrating gradually from the Neolithic period onwards, living in Southern Egypt, Nubia (modern day Sudan), Aethiopia (a broad region referring to what was known of East Africa and everything south of Egypt), and what is now referred to as the Maghreb and the distribution of dark skinned people in North and East Africa is comparable to modern times. These were not sub-Saharans but they were and are culturally and ethnically distinct from Berber, Arab and Egyptian peoples, with a well known example being Nubians.

There are in fact multiple burials of Roman African soldiers in Britain but whether they would be considered black today is uncertain as I understand it (someone else might expand here). In any case we can tell the place of origin of skeletons by studying things like isotopes in the teeth that show where a person grew up and where they lived, and phenotypes showing their ancestry, in addition to examining literary evidence like names and other biographical info that tell us about them. Females from North Africa have also been found in Western Europe implying that it was not just soldiers who moved around, it may interest you to know that the Egyptian goddess Isis was brought to Britain by the Roman Empire.

I also have to challenge the idea that ancient Italy was ever "homogeneous", there were numerous Italic, Greek, Etruscan and Celtic groups inhabiting the different regions and while we might lump all of the various tribes and city-states together as "white" this is anachronistic. The Empire itself was full of West Asian and North Africans who would not be considered "white" today, and Romans distinguished between Latins and other Italians, even Greeks were seen as a very different ethnic identity so saying Italy was "homogeneous" makes no sense.

That said, much like today foreigners made up a minority population in every region and Britain was mostly British, not Roman or African but ethnic Brits.

#What did ancient people think of race?

The idea that skin tone carries associated cultural traits with it and that this is a powerful determinative for individual behaviour and broader social trends is a relatively recent, albeit gradual, development. At the time of the Roman Empire there was no concept of "whiteness" or "blackness", there was no European identity to contrast with Africa.

Greeks and Romans both saw themselves as existing on the sweetspot of a continuum of cultural and physical attributes. Hippocratic environmental theory posited that cold, damp environments produced pale, large and slow organisms while hot, dry environments produced dark, small and quick organisms, this explained what was seen as peculiarities between wildlife and peoples. While Greeks and/or Romans were not as brutish or as physically powerful as their northern neighbours, or as effeminate and crafty as those to the south, they were of a perfectly balanced disposition and therefore culturally superior to outsiders.

The various reasons given for differences in skin tone vary from more scientifically inclined causes like environmental theory to mythological ones like Ovid's Metamorphoses in which a son of Helios crashes his father's chariot and burns the Ethiopians causing their blood to boil into their skin. Quite often, black Africans were used to contrast with Celtic and Germanic peoples as both were seen as savages but on completely opposite ends of the spectrum, although earlier Greek authors preferred contrasting Aethiops with Scythians, and Janiform vases often play on this theme by contrasting the forms of the barbarian.

What separated this from modern racism was they were not seen as separate subspecies or as being lesser by virtue of their skin tone. Much like with Celts they were often depicted in Romanticised or idealised forms in Hellenistic art as in this sculpture of a Nubian boy, and in literature like the Alexander Romance or the love epigrams of Philodemus they are portrayed in a positive light. This makes sense if we consider that modern ideas about nationality and race did not exist, the primary social advantage was citizenship but most people living in the Empire, even Italy, were not citizens which did not change until fairly late in the Imperial period. From the Hellenistic era to the Roman Empire the strongest aspect of identity was the cultural and linguistic background of an individual. The ability to speak Greek or Latin, to understand and identify with the culture came before anything else, even the original usage of the term barbarian simply denoted a non-Greek speaker. Individuals were treated according to their socioeconomic status, occupation, rank, and prestige, and there are numerous examples of dark-skinned individuals from Africa, Egypt and even India who did well for themselves and were esteemed in the Graeco-Roman world.

From Stilcho a Germanic general to the Severan Imperial dynasty of North African ancestry we know that quite a few non-Italians reached considerable heights.

Many authors mention the surprise with which individuals who had never met dark Africans had when they saw them, and this is only reasonable for a time when most people did not travel far unless they were in the army, a trader or very wealthy. People in rural regions would have encountered fewer people with black skin, and even out of Rome's cities Alexandria would always have a much higher proportion of blacks than Ravenna. Superstitions or fears around people who looked markedly different than you was supposed to be something people left behind at childhood, and although the exact percentage of people we would consider "black" is difficult to estimate (given the malleable nature of the definition and the relative lack of interest ancient sources have in describing skin tone compared to the modern fixation with it) Snowden argued the proportion was higher than what we would assume although still a small minority and it is undeniable that probably the most diverse occupation was the auxiliaries which conscripted non-citizens throughout the Empire. As it stands, Snowden's Blacks in Antiquity: Ethiopians in the Greco-Roman Experience is the most comprehensive study of "black" individuals in the Roman world and I recommend it to study the topic further. But the most important things he proves is that the idea that Romans would naturally discriminate against people based on colour is in no way evident, although the assumption that the ancient experience has to be analogous to the premodern or modern one is made about a variety of topics ranging from sexuality to religion.

Having established that people were not discriminated against based on colour, we have to ask whether racism is only colour prejudice or something deeper. Were Greco-Roman sources racist towards foreigners? Possibly, Isaac posed this question in The Invention of Racism in Classical Antiquity where he argued that our expectation that racism would naturally be between black and white peoples was further projecting onto the past and ancient "racism" was alive and well despite not revolving around the European/Other dichotomy.

The closest thing to modern racism that can be found is in the ethnocentric and xenophobic rhetoric of ancient civilisations, from the Greeks disdain for Persians to Roman propaganda against Egyptians and Celts during their wars with these people. Prejudices and generalisations about inherent traits Asiatics, Celts, Africans, Hellenes and Italians are present, so can we limit racism to colour or does it extend to a wider range of sentiments? Does racism require hatred or can it apply to all ethnic or cultural stereotyping and divisions? While these are not related to colour or continental origin, they echo the contempt and devaluation that is central to modern racism, however unlike modern racism the strength of these attitudes tended to wax and wane, the enemy of today is the friend of tomorrow and vice versa.

I recommend Snowden's work as well as McCoskey's Race: Antiquity and its Legacy discussing the xenophobia that she argues was a precursor to modern racism. Isaac's The Invention of Racism in Classical Antiquity is also a good source, and Thompson's Romans and Blacks is also useful. All of the above are generally well regarded but you might want to read up on the criticisms of McCoskey, Isaac and Snowden for a more holistic view.