I think what is left and right have been evolving since the 60s. Leftism is being fought over now between anarcho-capitalists vs labor while the right is being fought over between big business vs nationalists.
"Left" and "right" have been pretty arbitrary ever since the French Estates General set up their seating plan with monarchists on the right and republicans on the left. That fight, like all fights before and since, was really divided along multiple axes with overlapping but not identical motivations.
I don't think there's a single thing to be misunderstood, so much as a rough analogy between many different kinds of political battles. Anti-intellectualism does seem to present a kind of newish element to that fight, though I suspect it's always been present in various guises. (I will say that I'm particularly unhappy with the version of it that has dominated for the past 30 years or so.)
Left and right is not really useful. The issue is that there are multiple degrees of state control. But state control comes in more than one flavor. States want either to control what everyone thinks, or to own the economic output of all individuals, or some combination of these two. The state control axis is the most relevant, and its endpoints can't be labeled left or right.
Right, among leftists, some want an absolute state authority controlling all aspects of the economy, and some want absolutely no government at all. The common denominator is the socialization of the means of production (for whatever that means to different people).
Left/right is kind of a stupid spectrum because it's essentially compressing a great deal of dimensionality into a single dimension. And not even that, but "left" in the US means "higher taxes" where to the rest of the world it means "abolish private property and money."
> The state control axis is the most relevant
That's like saying "I think color is the most important aspect of art." I think different things are more important to different people, subjectively. That said, given where I land on this political compass (https://www.politicalcompass.org/analysis2?ec=-9.0&soc=-6.62) I'd say I do share your views on state control being important.
