Thought this was interesting—and not untrue!—but also weirdly quiet about the reality of the publishing business.
One reason the New York Times and the New Yorker (say) have "insane house styles" (i.e., are risk-averse about what and how they publish) is because they are actual businesses; the right-of-center journals and websites referred to are usually donor-funded passion projects.
Just ten years ago there were a half-dozen small, young, and flexible "left-of-center" publications that accepted pitches of all kinds and were instrumental in launching careers—many of the writers you read today in the NYT or the NYer etc. got their first bylines on the Awl or Gawker—but they've mostly gone out of business. It's quite hard to make money publishing writing in the 21st century, especially formally challenging stuff from new writers. (Just ask anyone who's tried to revive the Village Voice over the last 15 years.)
So on the one hand I would be careful about attributing any divide here to "culture" in some direct sense—the "culture" (of risk aversion, hierarchy, etc.) of a publication or an ecosystem follows from the funding structure and business incentives. And on the other I would be careful of regarding the (apparent) flowering of small right-of-center journals or publications as marking a real shift in publishing... the lesson from the "liberal" side of things is that you're only as daring and flexible and original and young as your business model allows.