How do I have anonymous notifications (phone, text, ...) on Android 4.3 like 4.1?
This is only a partial answer to my question, so I won't mark it as accepted just yet.

If you go to Messages / Menu button / Settings / Notification settings there should be a setting called "Preview message". Uncheck this and text messages will not show up in your lock screen.

I have not figured out how to do this for calls though.