I had a pretty rigorous and extensive course of biology in high school, we spent a lot of time poring over various details, but the word clade never even fell. (Granted, that was 1992-1996, so things might have changed.)
I only met the expression cladistics and clade much later in some popsci literature.
Most HN readers I'd wager. Regardless, "Trees are not a distinct evolutionary group" or "Trees are not all related to each other" or any number of other accurate or semi-accurate headlines are better than "There's no such thing as a tree".
I made a similar comment further up the page: I think some people massively overestimate the amount of general knowledge people have about biology. Like the article says, a lot of people are still at the 'did you know a tomato is a fruit??!' stage.
I think the first time I encountered /clade/ was in Bruce Sterling's Shaper/Mechanist stories. "Cicada Queen" was written in 1983, but I expect that I thought he made the word up for several more years.