The inside/outside dynamic is not the only part of the location that matters for the dangers these events present. The big protests mainly occurred in big cities and were mainly attended by locals. The Sturgis rally happens in the middle of nowhere, people come from all over, and then head back home to places that are generally more rural. Sturgis is therefore much more likely to spread the virus to people and places who wouldn't have had much exposure otherwise.
Also we can't have this conversation while ignoring the false equivalency of these two events. There is a fundamental difference in the urgency of attending a protest versus attending the Sturgis rally. If they both presented the exact same danger to the population, Sturgis would still be a more egregious gathering due to being an entertainment event. We are in the middle of a pandemic. We can cut down on these large entertainment gatherings whether it is Sturgis or Coachella.