Ross Douthat had a post on "The Missing Right-of-center Media" in which he noted that "outlets that mix political and cultural coverage" had liberal readerships; the other side, which he didn't say explicitly, was that outlets with conservative readerships were pretty much exclusively focused on politics. His proposed explanation is that "well-educated and well-informed conservatives are often businessmen (note the Wall Street Journal’s near-center position) whose reading interests are more practical and professional, who don’t cultivate a member-of-the-intelligentsia self-image, and who treat their media consumption mostly as a source of information rather than identity."
But political news and opinion is of no more practical value than cultural coverage (arguably less), so his explanation implies that there wouldn't be a significant audience for conservative political media, which there obviously is. It seems to me that there are two possible explanations.
One is historical: the "old media" model was to cover a range of topics, and most of the surviving "old media" have become politically liberal (the Wall St. Journal is an exception). So they have a mostly liberal but ideologically mixed readership (in the case of the WSJ, mostly conservative but mixed)--some who read them mostly for the political coverage, but others who don't agree with their politics but read them for other features. The "new media" model is to focus on one thing, and a number of conservative outlets have appeared to supply the demand. They have an overwhelmingly conservative audience.
The other is that it reflects demand: liberals like cultural coverage more than conservatives do. Douthat says something like this, although in pejorative terms--the "liberal clerisy" likes to "cultivate a member-of-the-intelligentsia self-image." Of course, if there is a difference of this kind, you could explain in a way that's favorable to liberals, or take the sensible course and say that you don't know why it exists.
There are a few surveys that have asked about interest in "cultural" things. One of them is a Pew survey from 2005, which asks people if they have visited the following in the last 12 months:
an art museum; a science or technology museum; a zoo or aquarium; a planetarium; a natural history museum; a public library. Unfortunately, the only questions on political views are ideological self-rating (liberal... conservative) and party identification. However, liberals are more likely to say that they have visited each one of those institutions. The differences for science and technology museums are not statistically significant, but all of the others are, most by a comfortable margin. The differences remain after controlling for education. There is little or no difference by party identification.
As I've said in several posts, a lot of people don't seem to understand the terms "liberal" and "conservative," or to understand them in non-political ways. But the relationships are so strong that it seems likely that liberals really are more interested in "culture."
[Data from the Roper Center for Public Opinion Research]