I do not believe it is far to say that people should stop watching football solely based on the fact that the sport is dangerous to players. The players are paid vast sums of money for their service and just as those that enter the military, there is a firm understanding that there is a possibility of injury.
Yes fans have a right to continue to watch and support American football even though there are dangers to the players. Fans are not making the players play, players are choosing to play. There are also a lot of other dangerous activities that have support like fighting, wrestling, strongest man, NASCAR
I think it is fine for fans to continue to watch American football, despite the risks to the players. All sports have some risk of injury, and the players are highly trained, and are fully aware of the risks they are placing on themselves, and it is up to the player to decide if he wishes to take the risk, not for a viewer to decide what is best for a player.
Yes they should the NFL needs to improve the equipment to reduce the amount of injuries that are happening to the players on the field. If they found helmets that protected the head more it would be beneficial. They need better padding also to protect their bodies and change the rules a bit and it will be safe again.
Yes, fans of American football should continue to watch the sport as long as it is played by participants who are informed of the risks involved and who consent to participate, despite these risks. Players should be well-advised of the known risks by leagues and teams, and research should be devoted to determining and minimizing risks to safety. As long as there is no dishonesty on behalf of teams, leagues, or owners, however, there is no ethical questioning necessary to enjoy watching an NFL game.