I think that you are making the same mistake that you are accusing healthcare workers and officials of making. You are assuming that these protests will "obviously" result in thousands more deaths because it feels that way to you. I believe that that's pretty unlikely, though, since there are probably fewer than a million protestors across the country. Many of the protestors are wearing masks and the protests being outside reduces the risk of spreading the disease. There will certainly be some spread due to the protests, but probably not nearly as much as at grocery stores or churches. You are also assuming that this is just about unjust police-involved deaths; it is not. It is about the many millions of negative interactions with the police and justice system that perpetuate poverty (police lying under oath, egregious sentences for non-violent crimes, etc.) I don't think it's a bad faith argument to say that correcting these injustices is more important than maintaining a totally strict quarantine.

The reason both sides talk past each other is because they have different values and different assumptions. Based on your post your first priority is preventing deaths and your assumption is that these protests will cause more deaths than they prevent. My first priority is living in a fair world, with preventing deaths being a close second. My assumption is that the protests will not cause a large number of excess deaths, but that they do have a high chance of moving our justice system closer towards real justice. I also am making the assumption that living in a fair and just society will increase overall health outcomes over the long term.

I believe that most (but definitely not all) people don't argue in bad faith, they just have different values and make different assumptions. There's not much that can be done about having different values, but better data can help every side have more similar assumptions, which should help opinions to converge somewhat.