Well, there are different levels of biological and racial differences, like species, subspecies and varieties or types. Its simple, there is not always some sort of dichotomy. Like if people like Barack Obama or Halle Berry claim they are "black", they obviously aren't "only black" if that term would mean Subsaharan African. The father of Barack Obama was, however, and he himself is mixed race and might identify with the African American ethnicity, which, in the local American context, being used to refer to itself as "black".
Its a prime example of when "race" truly becomes a "social construct": When the biological and socio-cultural identification being decoupled from each other.
Of course you are right about when someone mixed could be put in any "pure" category. The question is whether that's even necessary? In fact in many such instances going down to the individual makes sense again, because like North Africans, being obviously more West Eurasian than anything, without being "genetially pure". One can still distinguish the ancient ingredients.
Like Jovialis said: These are ingredients, whether one is pure or not. Its the obsession with purity which makes things absurd. If "a single drop" can make all the difference. That's in fact an American problem. In Brazil for example, there were and still are many categories for all kind of mixed individuals from different backgrounds. Even in South Afria there wasn't just "white & black", but in the USA, for quite some time, there was this strange dichotomy even for obviously mixed people. Blame it on the Jim Crow laws that Americans being so obsessed about purity and confusing biological reality with social constructs. Don't blame nature or natural sciences, not the present and not even (most of) the old anthropological one. Its wasn't studied anthropologists, usually, which were that obsessed with purity, even if they used ideal types for their theories.
We can define WHG ancestry genetically, and we can still determine where it survived, to which people it spread. Does it really matter that it doesn't exist in a "pure form" any longer? It still makes a difference for people to have this component and without these forager ancestors Europeans would not exist the way they do.
Same applies to Neandertal admixture, if we assume (what's very likely), that the hybridisation event was real. We can define Neandertal admixture, we can assess its importance for modern populations and how it influenced their evolution, even though pure Neandertals no longer exist for tens of thousands of years.
If you don't define the ingredients, you can't understand the processes involved to shape modern populations, dead or living individuals, and the genetic and phenotypical profile observable and measurable. It doesn't matter whether a person is pure or not. Every individual has its own genetic make up based on ancient or more modern populations. Even if they crossed each others path more than once, mixed more than once at different times, there is still a traceable and observable gene flow and ancestral make up for every population or individual.
Without defining the most important components and categories, things get just fuzzy and more amateurish. People still try to define and describe "racial" differences, even if they lack the proper terms, they just get more subjective and worse at it.
