That sounds scary.
Why would having every government department, hospital, doctors/dentists office keep your data separately, probably in some unsecured excel file or whatever?
When we have one registry for everything, they can keep it secure by having some proper security guys design and audit it, we can see who has accessed my data and when, etc. If a hospital would keep your health records in their own system then.. they'd probably have some low paid IT guy design something and leak it accidentally online.
10 years ago people would have called you paranoid now you're already too late
On the other hand, when these connected systems are in place it's not like employees can just tap your name and get the data, there is some Auth process with your eID/certificate.
It all boils down to people's trust in the government. In Scandinavian countries that trust is high. In Southern European countries it's very low (and much lower in the US).