What a stupid, hysterical claim. This "sensitive data" is just what's on your passport, fingerprints, criminal history, and terrorism flags (from European agencies), only for people crossing the border. I don't see how you could defend not sharing any of that.
...uhm You are happy to share your home address and everything else to securely identify you to a government acting increasingly erratic? Because I am not. I would be happy if terrorism-flagged people are shared across borders, but not everyone.
Remember once the dataset is there, it is not ever going to go away, regardless of who is in power