Despite the headline, it does not seem quite as bad as it sounds once you watch the video. I think the ropers actually did the best thing they could have done right then. The woman ran into the horses' space. That was foolhardy and endangered herself, the riders, and most of all the horses. Putting aide the legitimacy of the protestors' cause, you don't jump INTO a corral and start running around the horses. The guy with her looks like HE was the one who starting dragging her. The riders did not throw the rope over her - they encircled her and were moving her to the side when her associate runs in and yanks on it. I'd say the riders moved swiftly to prevent this woman from coming to harm. (though their main motivation was not likely HER safety. Someone ran in and they reacted immediately - as they should have done.
Really - if you are going to protest a rodeo, it is pretty stupid to jump INTO the ring and protest from there