I think this is easy to explain by considering that the meaning of left/right constantly changes over time. For example, how would you characterize somebody who is pro free speech, anti war, anti hegemony, pro equality of opportunity, in support of a color-blind society, and so on? 20 years ago that would have been an absolutely textbook liberal, today that is no longer the case.
So when we say left or right we're not really referring to any sort of static values, or even fundamental values. It all just keeps shifting and often in self-contradictory ways. So the terms just become a proxy for the ever-shifting divides in society. This makes it essentially a tautology that any fair sampling of society will end up divided on those terms.
The changing of left/right over time is largely because much of American society views politics through the lens of Democrat/Republican. On a broader level, economic left/right and authoritarian/libertarian haven't moved, but both parties kinda rotate around them over time. At the moment I'd say both democrats are moving slightly further left, and both parties are moving more authoritarian.
So when we say left or right we're not really referring to any sort of static values, or even fundamental values. It all just keeps shifting and often in self-contradictory ways. So the terms just become a proxy for the ever-shifting divides in society. This makes it essentially a tautology that any fair sampling of society will end up divided on those terms.