We'd like to make you aware of the new Real ID-related privacy options we've introduced to Battle.net. These options provide Real ID users with additional tools for customizing the service based on their preferences, enabling the ability to opt in or out of the Real ID "Friends of Friends" and "Add Facebook Friends" features or to turn off Real ID altogether.
To access these settings, log in to your Battle.net account at http://www.battle.net/account. From there, click on the "Settings" tab located at the center of the Account Management menu and select "Communication Preferences" from the dropdown list. The new settings can be found in the "Privacy" section of the Communication Preferences page.
So, if this was something you were worried about, you no longer have to be since they added some more customization.