If public pressure on corporations didn't work, then fast food restaurants wouldn't be selling healthier menu items, Tina the elephant would still be at Greater Vancouver Zoo, circuses and performing animal acts would not have been banned from many N.American cities, and lots of other positive changes would not have taken place in the world. Just because the Cloverdale Rodeo has been around for years, does not mean this event is exempt from the same changes that others have been forced to make in the wake of public pressure.
If companies know their decisions are having a negative effect on consumers spending in their business, they will change.