Colors are physically real and measurable, just like the different appearances of people and their different blends of genetic ancestry are real. But, there are, in principle, an infinite number of colors (which boil down to a photon wavelength) and there are billions of variations in human beings. An association of a particular set of photon wavelengths with a particular label is arbitrary and could be done different ways, and so is a racial category. Different labels often treat edge cases and outliers differently and the labels that cluster lots of variety into a modest number of words are inexact descriptions. But, that doesn't mean that color names have no relationship to photon wavelengths, or that racial categories have no connect whatsoever to appearance or genetic ancestry or even to something entirely culturally constructed like ethnicity.
Racial Categories Are Not Completely Divorced From Genetic Ancestry Clusters, But How The Boundaries Of Racial Categories Are Drawn Is Arbitrary, Changes Over Time, And Is Historically Contingent
What is socially constructed is the manner in which people cluster people with certain ancestry or traits, the way that they draw the line between clusters, and the social significance that is attached to the socially constructed small number of categories called "races" used in day to day life.
Racial categories are also not really personal psychological constructs. In any given society, the racial category to which an individual is assigned is, for all practical purposes, something that can not be changed by the individual, it can only be changed by changing society as a whole. (Some legal sources use a "self-identification" definition of race, but since the number of people who defy their socially assigned racial category is very small, this definition has little material impact except in cases of category mismatch where the categories are a poor fit to the practical way people identify and are identified in day to day life, for example, there are multiple plausible ways for a Mexican-American mestizo to identify "racially" on U.S. Census forms - white, other race, Native American and more than one race would all be logical answers since the more specific and accurate choice "mestizo" in terms of both self-identification and social assignment of racial identity, is absent.) Most inconsistencies in racial identification in the literature involve cases where people whose racial categorizations arise in one culture (e.g. in Latin America or other non-U.S. countries) are applied in another (e.g. a U.S. racial category question). See, e.g., here and here. From the second link:
Of those who self-identified as White, 98.4% were usually classified by others as White; of those who self-identified as Black or African American (Black), 96.3% were usually classified by others as Black; and of those who self-identified as Asian, 77.0% were usually classified by others as Asian.
For example, suppose that you put 100 Brazilians in a room. The vast majority of the Brazilians, perhaps 90-95% at least, would classify at least 90%-95% of the people in the room into the same Brazilian cultural racial categories. But, an American would classify those same 100 Brazilians into very different racial categories and different Americans might not do so quite as consistently as the Brazilians would.
These social constructs can also vary in specificity.
For example, one of the more silly racial categories in the United States today, is the notion of an "Asian-American" for which someone of Chinese ancestry is probably the "type example", but which also includes ethnically Japanese people, ethnically Ainu people from Japan, Filipinos, Mongolians, Koreans, Papuans, Southeast Asians, Indonesians, Burmese people, and South Asians (a group of people with extreme internal diversity in both genetics and appearance), whose shared ancestry is very remote and whose ethnic ties are even weaker.
Asian – A person having origins in any of the original peoples of the Far East, Southeast Asia, or the Indian subcontinent including, for example, Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, and Vietnam.
The precise racial classification of new clusters of admixed people is historically contingent. The way that people with some European and some African ancestry were classified in French North America, prior to the Louisiana Purchase, was very different from the classifications use by Anglos in North America. The French treated various proportions of admixture (e.g. mulatto or quadroon) as different racial categories, while the Anglos applied a "one drop rule" in their classifications. See, e.g. here.
Similarly, there were no people in the world who had what is now the predominant Northern European phenotype (i.e. outward appearance) until a little more than 5000 years ago. The appearance of a typical Northern European today arises from admixture of people descended from early Anatolian farmers, with a little extra local European hunter gather ancestry, infused with a whole lot of Pontic-Caspian steppe ancestry.
In the same vein, the appearance of people in Africa was much more regionally varied until the Bantu expansion in the last two thousand years. Most people who appeared physically very different from the Bantu people, like the pre-Bantu population of Mozambique, either went extinct almost entirely, or are now restricted to relict populations (like the Kalahari Bushmen a.k.a. the Khoisan, and the Pygmies of the Congo River jungle).
The extinction of people sharing particular blends of ancestry likewise leads to the cessation of the racial category they were once assigned to in the consciousness of people in their day to day lives.
There is no longer even a word to describe the particular phenotype shared by the pre-Bantu people of Mozambique. The most common word to describe the phenotype of the early pre-agricultural hunter-gathers of Europe, Cro-Magnon, is now only meaningful to a quite modest share of people knowledgable about anthropology, archaeology and human genetics. The word for the pre-agricultural people of North Africa, who likewise had a distinctive physical appearance that differs from modern North Africans, is now only known to specialists in these fields.
Ethnicity, While Strongly Correlated With Many Arbitrary Racial Categories, Is Not The Same As Race And Is More Important In Interpersonal Interactions.
As a social construct, the social significance of race is not separate from the social significance of ethnicity, two visually identical people in a social setting are often treated differently based upon the dialect, accent and visible religious behavior. The way that other people react to an Afro-Caribbean Catholic in a major U.S. city is likely to be quite different from their reaction to an Africa-American from Georgia, or an African Muslim from Sudan with a great deal of Bantu ancestry, or a recent immigrant to the U.S. from Nigeria.
Even subtle ethic differences, like those between European-Americans from the American Southwest and Appalachia on one hand, and those from the North of the United States, on the other, can take on immense political significance as they do in the modern United States, with a lot of those differences directly attributable to ancestral cultural differences between founding populations in the Colonial era. See, e.g., the book "Albion's Seed".
Ethnicity Is Not A Racial Category, But The Two Heavily Overlap
In my view, the American Anthropology Association Statement on Race (AAASR), while not really wrong, in a fervor to disavow racism, understates the extent to which racial categories are frequently strongly correlated with similar patterns of genetic ancestry, the extent to which social construction of racial categories is a natural and inevitable reality that meaningfully affects the daily lives of everyone in a society, the extent to which racial categories and ethnicity are strongly correlated in most places, and the extent to which racial categorization is determined at the societal level rather than the individual level.
Racial Categorization Is An Old Concept
The notion that race is a 17th century Anglo construct is ahistorical.
There is evidence of racial categorization being common place in ancient Greek, Roman, Egyptian, Sumerian, South Asian, Chinese and Japanese texts from as far back as written history goes.
For example, the ethnonym "Gypsies" adopted in the late Middle Ages, arises from the adoption of a broad racial category box that put Egyptians and South Asians, both of whom have a skin color darker than Northern Europeans and lighter than sub-Saharan Africans, and shared other superficial visual similarities, into the same category even though the "Gypsies" had no ancestral connection to Egypt. Classical Roman geographers two thousand years ago, also were conflicted about the similarities between and differences between Egyptians and South Asians.
There is even inferential evidence for racial social constructs with great social relevance among Southwest Asian and West Asian hunter-gathers.
Ancient DNA reveals similar levels of genetic differences between Levatine hunter-gathers and hunter-gathers in the Caucasus and Zargos Mountains only a few hundred miles away, to the difference between people from China and people from England today. There is also genetic evidence of strong endogamy separating the two populations. This occurred in an era before the first human village or chiefdom or temple had come into existence and when the primary political unit was a band of a few dozen people at most, i.e. these distinctions pre-date any meaningful sense of "politics".