Gray wants to connect New Atheism to Posivitism (presumably the Vienna Circle) and deprecates Positivism as "anti-liberal":
New Atheism, in Gray's view, is a cruder version of 19th-century Positivism, the philosophical position holding that the only real knowledge is knowledge acquired through the senses. ...Talk about ten pounds of shit in a five pound sack. Let's unpack this paragraph.
Gray says the Positivists were anti-liberal. Some were fiercely intolerant, because they believed that all knowledge could and should become scientific. Science seeks absolute, clear and logical truth, so once social truth is rationally arrived at, why should we tolerate error? (Compare this, by the way, to the anti-liberal Leo XIII's assertion that "error has no rights" -- a formulation that the Second Vatican Council elegantly reinterpreted to mean that error may have no rights, but human beings do). Gray said the original Positivists hated individualism and critical thinking, and believed that a universal convergence of scientific truth would also mean a convergence of values.
First of all, why talk about Positivism at all? It is definitely the case that the New Atheist writers in the major or minor canon have no special connection to Positivism, apart from the general connection of all ideas in philosophy. If anything, the scientific orientation of many New Atheists connects them more firmly to Karl Popper, who was not a Positivist, not a member of Vienna Circle, critical of Positivist philosophy, and known as much or more for his liberal political philosophy as for his work on scientific epistemology. We can conclude only that Gray is promoting the worst kind of ad hominem guilt-by-association bullshit. Anyone can read the New Atheist canon, the major canon is very readable and cogent; the Positivist canon is, however, hard to find, hard to read, and has very little to do with actual politics. By pushing the criticism to the Positivists, Gray makes his remarks difficult to refute.
And why too does a conservative blogger approve of Gray's criticism of Positivism as anti-liberal? Dreher makes his equivocation obvious: when he wants to condemn someone as being anti-liberal, he means "liberal" "in the sense that all of us in the modern West are liberals." So the charge is that the Positivists, although part of all of us in the modern West are somehow against all of us in the modern West.
But in what sense were the Positivists against all of us in the modern West? Wikipedia mentions the "the so called 'left wing' of the Vienna Circle, mainly represented by Neurath and Carnap, and Moritz Schlick. The aim of the left wing was to facilitate the penetration of the scientific world-conception in "the forms of personal and public life, in education, upbringing, architecture, and the shaping of economic and social life". In contrast, [Vienna circle leader Moritz] Schlick was primarily interested in the theoretical study of science and philosophy." Furthermore, "The Vienna Circle was dispersed when the Nazi party came to power in Germany; many of its members emigrated to USA, where they taught in several universities. Schlick remained in Austria, but in 1936 he was killed by a Nazi sympathizer student in the University of Vienna." The Vienna Circle was not exactly the backbone of National Socialism.
We can infer that Gray connects liberalism has something to do with the toleration of error. The anti-liberal Positivists were fans of science, science does not tolerate error, nor does "anti-liberal" Leo XIII. So, presumably, liberalism (as defined by Gray) does tolerate error. But what precisely do we mean by tolerating or not tolerating error? It is wildly ridiculous to assert that the Positivists, the scientific community, the New Atheists, or skeptics in general favor, advocate or approve of criminal, civil or any sort of punitive sanctions against people who make errors. What we assert is only that error should be criticized. (Intentional or grossly negligent lying is a horse of a different color, but even then the strongest sanction I've seen advocated (outside of ordinary laws against fraud, libel and slander) is calling liars liars and fucktards.)
Gray (if he is trying to make any underlying sense at all, and not just throwing pejoratives at random) is therefore arguing that liberalism and tolerance entails not criticizing error... and he then goes on, astoundingly enough, to say the Positivists hated critical thinking. Maybe Gray really is just throwing pejoratives at random; we can only wonder why he did not also accuse the Positivists of fucking sheep, beating their wives and mopery on the high seas.
Gray is descending into pure truth-relativism here. (Of course truth-relativism always permits criticism of the other guy.) This is a broad pattern in conservative and religious discourse: They criticize the liberals and atheists for their alleged truth-relativism but immediately retreat into truth-relativism when they're the ones being criticized.