I heard that, too.
It did occur to me that NFL contracts might have stipulations regarding player behavior that could tip the scales one way or the other, but I was more interested in the broader issue that so many people misunderstand First Amendment rights. The First Amendment gives you the right to speak. It doesn’t entitle you to a platform or an audience. And it doesn’t mean that employers have no say in speech that takes place at work (just ask any HR rep!).
In another twist, the NFL apparently receives some government funding. A clever lawyer might use that to argue that players’ protests are protected speech rather than speech subject to the rules of a private employer.