There are a few rules that I live by when it comes to social media.
Whether it's my boss, coworkers or people in my department, I always consider social media a "window" into my personal life. If I want to vent about work on Facebook, I better decide to keep work and personal separate. I choose to keep it separate because I choose to keep my personal life just that, personal.
A few things to keep in mind - if you go out to drink with people from work, most likely you are on your best behavior because you want to keep a good image in the workplace. Same thing with social media. That's just my opinion though, I know several people that do not make a connection between the two.
Now, as far as your manager... she needs to consider what I just said above. It needs to be kept separate. She cannot be "insulted' by something that you said on your 'personal' facebook page in the workplace. As a manager she needs to create a positive work environment and teach by example. Maybe the best way to approach it is to let her know you apologize that she was offended by what you posted, and to encourage her to delete your profile as a friend if she feels that is best for the work relationship.