Let's disagree to agree.

This is an admirable sentiment propped up with artifice. Everything from "We are one species" forward is, in my view, inarguable. But "there really is no such thing, scientifically, as race" is fundamentally disingenuous: it's like saying there's no such thing as "generosity" or "jealousy" because capital-S-science doesn't have formal definitions or standards for these qualities. Even worse, it actually obfuscates a basic principle of life science: that evolution is fluid; speciation is nothing but sufficiently distant cousinage. Except with a monoculture (like the Cavendish banana) defining a clade doesn't prohibit or discourage subclades. And denying subdivision of species is not merely idle sophistry: race-blindness would catastrophically diminish the efficacy of screening and managing sickle cell disease, Tay-Sachs disease, and similar genetic disorders.

Not surprisingly, the pugilistic Bill Nye above is quoted too restrictively: Mr. Nye supports his message re human unity with a more nuanced (and more entertaining) discussion of the science behind it.

We obsess about whether our dog is a pug-Jack Russell terrier mix with corgi overtones and an oaky finish. 'An approachable little dog.' Whatever. They’re all dogs, okay? And so the idea of a purebred is just a human construct.

Er... ok. Again, I take the point, but I think there's a difference between "a human construct" (i.e., a mental schema humans make up to explain something) and an actual thing humans actually constructed (i.e., Scooby Doo and Gidget*, via selective breeding). The problem comes when you start speaking as if "science" and human communication were the same thing:

If a [Papuan] hooks up with a Swedish person all you get is a human. There’s no new thing you’re going to get. You just get a human ... there’s really no such thing as race. There’s different tribes but not different races. We’re all one species.

Granted! But who said the word "race" meant "species"? I think the general public—insofar as they consider it at all and without resort to scientific terminology—understand "species" primarily as "members of a clade genetically similar enough to successfully reproduce." There is no way any common use of the word "race" today means the same thing. It is nonsense to proceed from the proposition that recognizing race denies the unity of the species. Bill Nye can draw a Venn diagram of this as easily as the next scientist. But he is a science populist/popularizer, a humanist, and (absent a skosh of evidence to the contrary) a Good Person, and he thus considers the ultimate message so important as to trump (not Trump—for there we are talking speciation) the finer points of science. I respectfully dissent.

Of course we must emphasize the universality not just of our species but of our entire biosphere. That we are all "in this together"—that the survival of life on earth depends on our species behaving intelligently in the broadest possible societal context—is the most important truth we have before us. To present bad science and popular myth, even in ultimate support of this overarching goal, is to act in bad faith—to betray the goal itself.

-----
* BTW, that dog is dead now.