Does anyone know from a privacy/data protection what are the laws/rules around someone taking your finger prints?
The rules are not about the taking of personal biometric data for a purpose that you give your consent for per se. Most data protection legislation around the world focusses upon the security of your data once you have provided it and to protect you from unauthorised sharing of that data with third parties that you have not been told about. When somebody takes your data they have to present you with a Fair Processing Notice (that's the UK terminology) that sets out what the recipient can do with it.
Of course, 'national security' usuallly renders that invalid.