It seems to me that over a billion people are fine giving their privacy over to Twitter/Facebook/Instagram/<insert other company> but not necessarily the Government (of any country).
People do care about it, they just don't think about it that often, or only think about people seeing their tamest online behaviour. Here's one recent example of where a privacy policy did capture the public's attention:
http://www.marketwatch.com/story/snapchats-new-scary-privacy...
There's also a big difference between not caring and caring, but feeling powerless to actually do anything about it.
For any of these larger privacy issues, most people are powerless to make significant changes. I can't prevent Google from driving its Street View cars by my house. I can't prevent Facebook from making shadow profiles about me. I can't prevent the NSA from conducting mass surveillance, etc.
I don't think it's a case of the public not really caring about their privacy, I think it's a case of them not fully understandind exactly what data is collected on them and how it can be used nefariously by companies and by their government.
We in the tech field tend to have an above average knowledge of these things but Joe Public is very ignorant of it.
I believe if people knew exactly what was being collected and how profiles of their entire lives, their thoughts, their actions and their potential thoughts and actions, they would be a lot less happy about it.
The problem is educating people who probably already have enough shit to think about in their own lives and convincing them that this isn't all conspiracy theory.
It's a monumental task.