The cancelling of school/sports in Spring was proactive. A move that generally should be applauded by all. As one meme out there put it, "We have to take necessary steps before they seem necessary. And if it works, people will think we over-reacted. We have to be willing to look like we overreacted."
As for your indictment of protests as the leading reason for the increase, if so we would be seeing the spikes in places like Minneapolis, NYC, D.C, Chicago, but we aren't. We are seeing it Texas, Florida, and Arizona, states that opened the bars/stores early. If I am being completely fair, there is some evidence to suggest that the reason these states are increasing is because people don't want to be out in the heat and instead inside in the Air Conditioning where it is easier to spread.
You can't limit protests, there is no admissions gate; there is no entrance. Most protesters (while not following social distancing) did seem to be wearing masks.
My worry for sports isn't necessarily the fans/bands/cheerleaders (they wouldn't barred from games), it is the players themselves. When you are 2 inches from someone, it is harder to not breathe, sweat, etc. on them,