Putting off the New York Times specifically for a moment, this is a "no true scotsman" fallacy.
Example:
"The New York Times is not that left-wing, and all centrists realize this."
"Many centrists think they are getting more left-wing."
"No true centrist would think that, therefore, they aren't centrists."
"Many vegans think it is vegan."
"No true vegan would think that, therefore, they aren't vegans."
No True Scotsman is about a particular form of reasoning, not any sentence that includes the word "true". It's a form of ad-hoc rationalization where someone rejects counterexamples out of hand. ramraj07 wasn't really making a generalization, and the rejection of the "counterexample" was neither ad-hoc nor unjustified. Many people outside the U.S. have always viewed American liberals as right-wing, and this is justified because American politics actually are right-wing compared to much of the world.
I think the pandemic played a big number on entitled people suddenly being asked to do things out of their choice and obey rules everyone else is subjected to, and polarize them against socialist ideals than before.