Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
Note the language Congress shall make no law… abridging the freedom of speech… or the right of the people to peaceably assemble. The First Amendment draws a distinction between freedoms and rights. So what is a right and what is a freedom? A right is an inalienable privilege that rests with the person. For example, a person cannot be compelled to undergo a beating. Neither a governmental nor civil actor can compel a beating without being subject to legal consequences. Even actors with limited authority to use force (parents administering corporal punishment or law enforcement effecting an arrest) must limit the use of force to no more than necessary.
A right can also be an affirmative action, such as the right to remain silent or the right to vote. If an individual exercises their right they are not subjected to consequences for doing so, and cannot be compelled to forsake the right. If an actor is subject to consequences for an action it is not a right.
A freedom is similar. A freedom is an activity the government cannot prohibit, but an actor is not shielded from consequences for acting. Also, a private entity does not have to allow the activity on their premises. If you miss work to go to church or write a libelous blog your employer can discipline you for doing so. You are free to engage in the activity, but not free from the consequences that follow.
So the anthem protesting, is it truly a right as is being claimed? The answer is undeniably no. Any owner could impose discipline as they see fit for the protests. That is the earmark of a freedom not a right. Which brings us to the question of the boycott. The boycott is a protest against a perceived injustice just as the anthem protests are. The NFL anthem protests and the boycott in reaction are both forms of peaceable protest. They are flip sides of the same coin. Since it is the flip side of the same coin the NFL and all associated should be equally accepting of the boycott. They aren’t, which belies the argument that their actions should be accepted as exercising their “right” to protest which justifies the boycott.