And, I share that distrust of government and belief in rugged individualism and it makes me uncomfortable to give out information like that when I know that the government will have easy access to it., but I also recognize that there are times when small "sacrifices" need to be made for the benefit of society as a whole. And, in the case of contact tracing, for my own benefit as well. I mean, if we are going to open up the economy, certain "sacrifices" are going to need to be made to do that. Some people will be sacrificing their lives so I don't think it's unreasonable to ask people to write a name and phone number down when they decide to have a meal with service at a restaurant. In that light, my discomfort with giving private information to a third party that might give it to the government doesn't really seem all that important.
And, it completely complies with the balancing test that SCOTUS has established over hundreds of years of jurisprudence. The fact is that rights will be limited in some ways by almost any government act. The question then becomes how important/fundamental is that right and how narrowly tailored and reasonable is the thing that is being done to violate that right. In this instance, I see the violation as very, very minor and the method to be pretty narrowly tailored for a very important purpose - contact tracing. It's not like they are even checking ID's to get the info. They don't even get it unless their if someone there tests positive. They aren't collecting all of these logs.
We have allowed many other violations of what I think are much more important individual rights to happen for must less compelling reasons.