I'm not sure if this is a bug, but on the Facebook Stack Overflow homepage the elements in the right bar aren't all facebook-specific. My favorite/ignored tags cover all of SO. The recent tags are specific to facebook, but the recent badges aren't
All user settings are inheritted from Stack Overflow. Your accounts aren't distinct.
Badges, being per-user, are also not distinct between the sites.
This is very much status-bydesign. Facebook.StackOverflow is a view onto Stack Overflow, not a truly separate site like an SE 2.0 is.