More information on this can be found in a 2013 letter from Howard Schultz, here.

Specifically from the letter: Our company’s longstanding approach to “open carry” has been to follow local laws: we permit it in states where allowed and we prohibit it in states where these laws don’t exist. We have chosen this approach because we believe our store partners should not be put in the uncomfortable position of requiring customers to disarm or leave our stores. We believe that gun policy should be addressed by government and law enforcement—not by Starbucks and our store partners.