Apparently. A comparison of bands "Liked" on Facebook and the political affiliation of the Facebook profile found that some music was more usually liked by Democrats and other music more by Republicans.
As you can see from this graph, members of << your preferred party >> have far superior musical taste, preferring such talented artists as << band you like >>, whereas << opposed political party >> lacks taste entirely, preferring talentless hacks like << band you hate >>.
Analysis of data from Echo Nest, an API that provides data about music, also found differences in the preferences of Democrats and Republicans. Analysis of Echo Nest data found that Republicans had less diverse musical tastes.
However, the findings of Echo Nest seemed to contract analysis of Facebook likes. For example, Democrats consistently like The Beatles on Facebook, but Echo Nest found that the Beatles did not have a strong partisan association. So, while there seems to be a difference, it is not clear what that difference is. A quick Google search will turn up a whole number of analyses finding differences between the musical tastes of Democrats and Republicans.