Asserting it as a "fundamental right" raises the bar on what restrictions can be put. But reasonable restrictions can still be put.
A separate bench of the SC is now going to test the validity of the Aadhaar Act on the basis of whether the restrictions are reasonable in the light of privacy being a fundamental right.
Edit: The Aadhaar Act is an act that allows for the government to collect biometric and other personal data that can be used to identify an individual for various services (including but not limited to governmental benefits).