The continuum fallacy is an especially bad one because it's really two different ones combined: a biological one and a geographic one. The biological continuum fallacy is the pretense that there's a vast number of people in expansive populations over broad areas of the globe possessing various mixtures between the identified groups of traits in all possible ratios, even though what's actually been mapped out is clear distinct clustering of consistent traits within broad regions with only narrow border zones of any mixing at all (and even there, the mixing ratio usually stays pretty lopsided toward one group or the other).
But there's also a geographic continuum fallacy, the pretense that human populations have never been isolated from each other, as if there were simply no such thing as an ocean or a desert hundreds of miles wide, or as if people routinely cross those as casually as a stroll through the woods or prairie. And the strangest thing about that is the fact that human genetic distinctiveness or the lack thereof between two locations tells you pretty well how isolated they were or weren't. In what was once Gaul, for example, there's no way to identify genetic groups descending from the Vandals, Ostragoths, Aedui, or Helvetii, or even to separate Celts from Germanics, and we still can't tell which of those two groups, if either, the original Belgae might have been a part of. In the Middle East, the descendants of the people of Ur and Akkad and Lachish are completely melted into the general Middle Eastern pot. THAT is what happens when there really is no isolation and no genetic grouping but a smooth continuum of mixing. And that's how they're claiming to think the whole world works. They're not just race deniers; they're also geography deniers, their assertions depending entirely on there simply being no such thing as geography.
You keep acting as if those are two separate things instead of the very same phenomenon at different scales. What are you claiming races are, other than rather large families? (Another odd thing about the denialist case: perpetually insisting on using their own private little made-up ad-hoc redefinition of the word "race" that nobody else uses and no dictionary contains, which must call for some additional requirement above and beyond any of the real ones, but never even getting around to specifying exactly what it is, nevermind actually giving any support for it as the definition.)