When the University of Missouri’s football team vowed to stay off the field until administrators met the demands of student protesters, defensive end Charles Harris grasped the national implications earlier than most. Wearing a shirt with the anti-police-brutality slogan “I can’t breathe,” he told reporters in 2015, “Let this be a testament to all other athletes across the country that you do have power.”

Mr. Harris, who now plays for the Miami Dolphins, heeded his own call. Last September he locked arms with other players...