Earlier quoted context omitted.
Perhaps we should base our judgments about the issues under discussion by the plausibility of the claims being made, the evidence supporting them, the likely consequences of different possible courses of action, and our values, rather than whether the proponents of one or another point of view hail from the upper class or the lower class.
Webster's says the definition of classy is "having or reflecting high standards of personal behavior".
Etymonline says, "pertaining to or characteristic of a (high) class," from 1891. https://www.etymonline.com/word/classy GCIDE says, "having elegance or taste or refinement in manners or dress," and "exhibiting refinement and high character. Opposite of low-class." WordNet says, "Elegant and fashionable." What brings all these definitions together is that something is good in the particular way that the upper class values.
It's true that many people who admire the manners of the upper class consider their behavior standards to be "high standards", and they certainly are demanding standards. But "classy" is not used to describe conformance to any demanding standards of personal behavior, such as a soldier's enthusiastic yelling and physical fitness, Clarence Darrow's unyielding advocacy of the welfare of the world's poorest, Feynman's profound mathematical learning and epistemic humility, or the brutal, unvarnished honesty demanded by Dutch society. As you know if you are a native speaker of English, none of these are considered "classy", however demanding they may be, because they do not belong to the [English and North American] upper class, which demands very high standards of etiquette, euphemism, diplomacy, fashion, and stoicism. Those virtues are "classy"; the other virtues I described above are not only not "classy" but in many cases positively opposed to "classiness".