Earlier quoted context omitted.
I wouldn’t use the term misandry because they also are interested in damaging women. “Turbowoke”, sure but we’re really just talking about mainstream American elite culture which is progressive. And young men are a particular target because they are generally the main threat to the status quo. Basically the NY Times is precisely an agent of the status quo.
I'm going to go out on a limb and say the institutional paper that lied to get us into the Iraq war isn't "turbowoke". The NYT is a propaganda outlet for the military industrial complex, not some sort of leftist activism.
The Iraq war was predicated on the idea that you could or should “bring democracy” to Iraqis, this is fundamentally progressive view of the world.
An actual conservative approach would be something like 18th and 19th century European colonialism.