His demand for Mr. Kaepernick’s silence came two days after The New York Times reported on another form of silence that comes with the privilege of dedicating your life, breaking your body and soul, to be in the N.F.L. Doctors, it said, had found a severe level of the degenerative brain disease chronic traumatic encephalopathy, or C.T.E., in Aaron Hernandez, the 27-year-old former New England Patriot who committed suicide in April while imprisoned on a murder sentence. His brain showed the kind of damage usually seen in players in their 60s.

C.T.E.’s toll on players’ health – a recent survey found C.T.E. in the brains of 110 of 111 former N.F.L. players examined — was of no concern to Mr. Trump. At a political rally in Alabama on Friday, the president complained about referees penalizing teams for excessive violence. Demonstrating with his fists colliding, he referred to a “beautiful tackle” that earned a 15-yard penalty. “They’re ruining the game,” he said.

He dismissed a fear that has led thousands of parents to keep their children from playing football, as casually as he disregarded the fears of Mr. Kaepernick for the safety and dignity of young black and Hispanic men off the field.