A lot of the confusion comes from the 'herd immunity strategy' also being known as 'flatten the curve' or 'mitigation' depending on who's talking and when. https://twitter.com/Birdyword/status/1350051885663870979
Herd Immunity, Flatten the Curve, and Mitigation describe the same actions and assumptions: you can't stop the disease infecting most people (that's Herd Immunity), but you can spread out the infections up to the herd immunity threshold to keep the peak below hospital capacity
You can find lots of people saying they were against the 'herd immunity strategy' but who also endorsed this diagram, which is the same thing- as shown in the WHO briefings and the New York Times
The differences are in the hearts of the planners: under 'herd immunity', planners are thought to be coldly indifferent to death, while under 'flatten the curve' they regret each passing deeply, and 'mitigation' is sort of in the middle
I think I've understood the nub of the confusion- people never stopped to ask *why* the infections eventually declined in this model- the acquisition of herd immunity!