No, as both the 49ers and the NFL are private entities, they could take disciplinary action against Kaepernick without violating the U.S. Constitution. (In fact, the Santa Clara County Police Officer’s Association is demanding that disciplinary action be taken or its officers may not provide security at future 49ers games.) However, Kaepernick may be protected by the Players Association’s collective bargaining agreement with the NFL, which does not seem to bar his conduct. Despite the misstatements of many (including President Obama), Kaepernick’s conduct is not protected by the U.S. Constitution from punishment by the 49ers or the NFL.
Unlike the NBA, which requires its players to stand during the National Anthem, the NFL has never had such a rule. Most of the NFL’s restrictions on speech are directed against unsportsmanlike statements to an opposing player or team, excessive celebration, and unapproved personal messages “in writing or illustration” – and not by demonstration. The players’ collective bargaining agreement may not allow disciplinary action by individual teams based on a team rule that has not been approved by the League. Thus, if the 49ers were to take disciplinary action against Kaepernick based upon his actions, he could file a grievance with the NFL Management Council against the 49ers to seek to reverse the decision.
Some have speculated that the 49ers are avoiding comment concerning Kaepernick’s actions to distance any decisions concerning his employment from his possibly-protected conduct.
While many have wrongly assumed that the U.S. Constitution governs every aspect of the employment relationship, private employers have considerably more discretion than state actors.