So its a trade off, would you want to trade privacy rights to right to live and right to move? For me, it is yes.
In addition, we know that we can reduce the risk of privacy infringement by designing the system properly, as they are doing it here. We could also use block chain technology to implement the database so that no central authority can know which exact individual has been to where. The database could also not store personally identifiable information. We could use cryptographic computing techniques so that no one, not even the software engineers working the project can know which person has been to where.
I know people are scared about the potential privacy infringement here. But if we don't try to come up with effective ways to stop the spread of the virus, there are people dying due to getting sick. And there are families who could not feed themselves because we shut down the economy.