If it feels like there is a steady stream of fresh outrage over consumer-brand gaffes, it may be because companies have become more adept at managing controversy than at pre-empting it.

Over the past year, H&M, Adidas, Reebok, Mercedes-Benz, and many others have faced swift backlash for offensive products or ads. As the reach of social media amplifies brand missteps, companies are finding they must develop new tools to handle the fallout from global online criticism.

“The...