If you go read it, which I don't recommend, you'll discover Sullivan is no conservative. Apparently he differed with the zeitgeist at NYM because he dislikes something called "critical theory," which is Neo-Marxist. To save you the effort, here are his progressive bonafides in a paragraph.
“Conservative” in my case means that I have passionately opposed Donald J. Trump and pioneered marriage equality, that I support legalized drugs, criminal-justice reform, more redistribution of wealth, aggressive action against climate change, police reform, a realist foreign policy, and laws to protect transgender people from discrimination. I was one of the first journalists in established media to come out. I was a major and early supporter of Barack Obama. I intend to vote for Biden in November.In other words, the establishment at NYM concluded Sullivan was the wrong kind of progressive - not an actual conservative nor even a centrist - which confessional distinction he takes pains to elucidate.
I imagine it was like serious evangelicals deciding they could not make common cause with a devout Mormon. All true believers but with different understandings of what pleases God.