The attitude of "mestizaje," though imperfect, has a lot to teach the U.S.
"Do the lessons of Mexico’s experience with mestizaje have any chance of influencing how the U.S. conceives of race?". Let me answer, no. Race (in the USA) as an ideology is far to profitable for the left to ever give it up.
Maybe more to the point: people will be people and admixtures are far and away the dominant trend going back to neanderthals and modern humans. The problems begin when governments get into the categorization business in order to divide and conquer the populace and distract people from their shocking incompetence, greed and hypocrisy. Nothing good has ever come of this process, which has all the science of phrenology and all the historical rigor of a comic book.
I fully agree that there is a lot to learn from Mexico's more causal approach to race. In my experience i is true that there is a small, wealthy elite that is white. But the vast majority is an indigenous/white mix across a wide spectrum of ratios, or entirely Indian. If they want to level down the small white elite, that is understandable. But to launch a US-style program of dividing everyone into oppressors and oppressed based on race would be completely incoherent. Of course that hasn't stopped US-influenced woke Mexican academics from trying. The race grift business is very tempting.
Racism as we know it is a novelty, developing in the 18th century in response to the Atlantic slave trade. It didn't exist in the Roman empire. Romans were hardly enlightened--they kept slaves, enjoyed blood sports, maintained a hereditary aristocracy, and despised 'barbarians'. But race is we understand it they did not get. American-style racism is an anomaly. You don't have to look to Mexico to find an exception. Look to the entire Western world (and probably beyond) until the 18th century when slavery was restricted to Africans and their descendants, racist theories arose to justify the practice, and pseudo-science of race was invented in the century that followed to provide it with 'scientific' backing.
Mexico is, as the author notes, racist and fetishizes skin color even though it doesn't, like the US, fetishize racial 'identity'. Look to the Romans for whom race as such was trivial, as it should be.
But what is the extent of discrimination on the basis of skin color, especially in the labor market? In Peru the lighter your skin color the more likely it is that you will get hired.
I'm looking at the (Anglo-)European world through European eyes, in particular the way in which a local feature of slavery in the Anglo-European world and, in particular, in the US played out in motivating a particular local form of racism.
Slavery is hardly a novelty. But the way in which it played out in the Antebellum American South as a condition limited to Blacks--in fact a default for Blacks who were viewed as enslaved unless they could prove themselves free was a novelty. Add to that the pseudo-science of race promoted in the 19th century to provide a 'scientific' justification for Jim Crow. The Peculiar Institution in the US was historically peculiar.
I'm not sure what your complaint is. Is your suggestion that the very idea that there is racism is 'woke' BS? That Black people are in the aggregate are intellectually inferior? Or what? Inquiring minds want to know.
How about a "Multiracial" Census category that is NOT limited to Latino "mestizos" and "mulattoes"?
Latinos and Their Escape Hatches