As occasional sparring partners over issues like white privilege and income inequality, Fox News anchors Bill O’Reilly and Megyn Kelly are accustomed to not always seeing matters the same way. So it was that the two stars of Roger Ailes’ network parted ways over a recent New York Times Magazine profile of Kelly. The largely glowing piece, by the magazine’s Jim Rutenberg, depicts Kelly as a serious, hard-charging journalist, unlike some people featured on the nation’s premiere conservative network. During Monday night’s “O’Reilly Factor,” the host dinged Rutenberg’s profile as a “puff piece,” bemoaning that other Fox personalities don’t receive...