I've read quite a a few editorials as well as main articles about excessive speech policing, primarily at colleges. There's plenty of reporting about self-destructive policies of the Demorcats and warnings about playing into Trumps hand. Also, the "NYY picks" of comments about articles are generally commenters complaining about illiberal trends.

I don't read cover-to-cover so I might be getting a selective view. My general impression is that the NYT is trying to satisfy it's generally older, whiter readership by weighing in against wokeness.

NYT runs a token moderate liberal article once in a while to represent the "right wing" viewpoint so they can argue that they're a balanced, neutral news source, which some take to mean they are "anti-woke".