In Yoga and the Roots of Cultural Appropriation, the term “people of color” is repeatedly capitalized, though the names of other protected classes are not:
Meanwhile, in order to uphold the foundation and on-going functioning
of white supremacist and racial capitalism, white people are taught to
be ahistorical and emotionally repressed. In order to maintain the
status quo, white people are taught to sublimate and anesthetize
feeling. To feel — whether joy, sorrow, or grief — is to be counter
cultural in this country. Dominant culture teaches white people, as
well as People of Color, to numb through materialism, consumerism,
entertainment, prescription and hard drugs, and alcohol. It also
socializes white people to consciously or unconsciously misuse power
and relate to others from a false sense of superiority.
Especially during this time when the underbelly of capitalism — white
supremacy, cisheteropatriarchy, and xenophobia– is being exposed, it
is imperative that everyone, especially those who have access to
spiritual practices like yoga, ask difficult questions of ourselves
and one another. We must ask, in what ways are we complicit in a
system that harms People of Color, queer and trans people, poor
people, people with disabilities, and immigrants? Despite our best
values and intentions as individuals, our actions (and inaction) are
inherently connected with a system of power, privilege, and
oppression. If we want to honor the full yoga tradition and live into
our values of love, unity, and fairness, we must examine the ways we
are upholding “business as usual.”
Should the term be capitalized?
John Hopkins doesn’t capitalize it in its style guide. It doesn’t mention capitalization of the phrase specifically, though it opposes the capitalization of “white” or “black” in most circumstances. An NPR article about the phrase doesn’t capitalize it, nor does the Wikipedia article about the phrase. Wiktionary doesn’t have an article explicitly about the phrase, describing its capitalization, and none of the matches from onelook that I looked at discuss its capitalization.
Related questions: Are “white” and “black” ever capitalized when referring to people? (summary: style guides differ) and In an Australian context, should “Aborigine” be capitalised? (summary: if you’re talking about Australian Aborigines, yes)
I tried looking at Google NGrams, but while it gave statistical data on the frequency of “People of Color” versus “people of color”, I couldn’t do a search for texts containing a specific capitalization.
The phrase “people of color” is not a proper noun and should therefore not be capitalized.
It is worth noting, however, that this rule is often broken, even in formal writing. It is common for authors to capitalize common nouns if the author is trying to draw attention to the noun. This practice is not prescriptively correct, but it is common, especially in writings about technology and social groups.
The example case given in the question has special considerations due to its social nature. When capitalizing a term used to describe a group of people when the term should not ordinarily be capitalized, it is advisable to capitalize all terms used to describe groups of people in the same writing, lest the author be accused of preference.