Popehat is pretty clearly against what he defines as "cancel culture," and the NYTimes article is primarily about journalists and elite opinion writers not liking backtalk from their readers.

This seems like another instance of what Dan Gackle refers to as "notice-dislike" bias: you're unlikely to notice as much when people say things you don't find objectionable, but notice acutely when they say things you find problematic. We all have that bias; it's a limitation of our cognition.