On principle, nobody should like this. It feels invasive. But living in a society is also about compromise and this is aimed at an actual problem. Is it a big enough problem that you have to control everyone?
I think this debate has more to do with the following. We don’t trust companies with information about us and we don’t like feeling our government is behaving like the Stasi. And we are not sure if company A or company B will use gathered information for only this thing specifically or if they are harvesting as much as possible for anything they can think of in the future. The police are allowed to search our homes, our digital life should be the same. It is then about reducing abuse of power and being in control of what companies collect.
What if we trusted a company to only do what they said they would and if they didn’t, they would be fined or otherwise punished? Would that change our opinion? Perhaps. Still don’t want anyone to just “look through my stuff” either. With these sort of things, you risk making regular citizens feeling they are being investigated, that they are doing something wrong and the result could be less openness, not more. Increased distance between those who rule and those that are ruled, not less.