That is a misconception that is common among the low information public. Most Starbucks stores are frequented by a demographic typical to the local community. You go into a Starbucks in Texas (outside of Austin) and you will probably find mostly conservative middle class professionals and possibly college students. If you were to poll the political leanings of the clientele you will probably find about a 60% or more right-of-center leaning position, which is representative of the local community. If you happen to choose a store in Austin, or in downtown Houston, that would probably flip the other way based on the liberal leanings of those communities.
That's a good point - I live in NYC, so perhaps my perception is shaded by the typical clientele around here. However, as true as that is with regard to an individual Starbucks store, Starbucks stores tend to be more concentrated (both in absolute terms and per capita) in urban and coastal areas. There are some exceptions (Texas is a big one), but that is the overall trend. So, in the aggregate, I would still think that their customers are more left-of-center than the U.S. population as a whole, perhaps significantly so.