Libertarians disagree with progressives about markets and with conservatives about "values", and that is really that.I think he's dodging the issue by putting "values" in scare quotes -- as if "value" judgments had no overlap with markets -- so I'm going to read the sentence without the quotes. This brings out an obvious inconsistency: if libertarians and conservatives agreed about the probable outcomes of markets (or anything else) and disagreed about how to value those outcomes, they would disagree about policy. Since they agree about policy they must have either common values or inconsistent forecasts -- for instance, some libertarians believe in trickle-down economics whereas conservatives don't really want wealth to trickle down.
The debate about "liberaltarianism" has brought out some of the bizarreness of libertarianism as an "ideology." To set up a contrast, conservatism in the typical, Ross-Douthat sense is a complex of things, based around the notion of a body politic: (a) a belief that people ought to behave in traditional, "normal/natural" ways -- these change over time -- and that such behavior should be encouraged or enforced; (b) a belief in social hierarchies, currently the family, previously the feudal extended family incl. servants that are in some sense "personal," i.e. that are maintained by stronger than commercial bonds (being personal, such bonds are exclusive, hence the xenophobic streak); (c) a sense that most of the existing order is just, and that malcontents are (currently) freeloaders or (formerly) people unhappy with their station or (eternally) Deviants. Populism is quite close to this, but instead of (c) has (d): the body politic is sick because of a cancer (deviant/freakish behavior at the head) or because of invading outsiders. Similarly, classical liberalism is a complex of tendencies based around the notion of the explorer: (e) it values freedom, individuality, and self-fulfillment; (f) it has strong anti-hierarchical tendencies, and is anti-feudal -- it prefers contractual to personal relations; (g) it is xenophilic (the "explorer" strain) and stands for the individual against the mob, even when the mob has a point (e.g., murderers and rapists). In addition, some classical and most modern liberals believe (h): the penalties for failure should be limited; everyone should be guaranteed a decent standard of living. Obviously each of these ideologies comes with a certain class identification -- conservatives with the small businessman who's a "pillar of the community" and liberals with travelers, scholars, and to some extent "The Other" in general.
You can't describe libertarianism in these terms at all. Being a libertarian is more like being a prohibitionist than like being a liberal or a conservative -- it's an agenda without a specific worldview. (Many libertarians dishonestly pretend that getting rid of government will make life better for everybody; this, however, just reinforces my point.) Of course it's possible to be a libertarian conservative -- you might believe (e.g.) that the government is weakening "local communities" -- or a libertarian populist -- if you think the govt. is run by special interests and actively oppresses the poor -- or a libertarian liberal -- if you think the govt. is basically a wiretapping agency. None of these ideologies is about government in any direct way -- rather, they're about desirable and undesirable outcomes. It is admittedly true that the relevant political parties have partly been hijacked by narrow interest groups that have little to do with worldviews per se; libertarians make a perfectly sensible pressure group; but there are excellent reasons why more self-aware pressure groups like AIPAC don't agonize over whether to think of themselves as liberal or conservative.