When it comes to what is allowed in terms of protests, American Constitutional law, labor and civil rights legislation, as well the NFL player's union Collective Bargaining Agreement all provide significant protection to a player.

A confluence of bedrock laws are on the players’ side. Stifling the protests would be illegal.
Start with the Constitution. Under the First Amendment, which protects free speech and free association, the president of the United States could not enforce a law that, say, required football players to stand during the anthem. During World War II, the Supreme Court struck down such a demand for a flag salute during the Pledge of Allegiance. ...

But it’s not just the Constitution that protects here, because the players also have rights as workers, rights they have been asserting both through the original protest and to rebuff the backlash. The New Deal of the 1930s and the civil rights movement of the 1960s saw landmark laws passed to bring into the private-sector workplace many of the constitutional values that constrain government action. These values include not only free expression and association but also the race and gender equality of the Equal Protection Clause and the 13th Amendment’s commitment to race and labor freedom. One leading example of these laws is the Civil Rights Act of 1964, Title VII of which bars race discrimination by private employers. ...

Title VII protects workers from retaliation when they oppose what they reasonably perceive to be race discrimination, even if someone else can reasonably disagree and even if a court ultimately sides with the skeptic. ...

Finally, there is labor law, passed during the Great Depression to reorder work and balance power between management and employees. The National Labor Relations Act protects employees who engage in “concerted activity for mutual aid and protection.” This covers not only union activity but also employees’ political advocacy around issues that affect their lives as employees. ...

The anthem protests are exactly this kind of advocacy, for three reasons. First, when black players protest police violence directed at African-Americans, they are targeting something that can impact their work lives even if it transpires off the field. Second, the N.F.L.’s contract with its players repeatedly asserts that their job involves more than what happens on the field. Having defined the job as a public one, the N.F.L. must accept that players’ public advocacy cannot be cordoned off from their role as employees. Third, many anthem protesters are now taking a knee to support teammates threatened with discipline, an act of solidarity at the core of labor law’s protection.
https://www.nytimes.com/2017/10/17/o...-protests.html


In the case of the NFL, the Collective Bargaining Agreement offers further protection to players. Although Kaepernick, because he is the plaintiff in the collusion case must provide the burden of proof to show that collusion occurred, has the right to depose the NFL owners, which has already begun, to look at team emails and other club information to support his case.

As part of the CBA, NFL players sign a Standard PlayerContract for a term of one or more years.74 During the life of this contract,a team may only remove a player from its roster if his “skill or performancehas been unsatisfactory as compared with that of other players competingfor positions” or, arguably, if the player has “engaged in personal conductreasonably judged by [a team] to adversely affect or reflect on [theteam].”75 However, language in the CBA, which takes precedence over theNFL Standard Player Contract,76 limits the maximum penalty an NFL teammay impose for “conduct detrimental to [an NFL club]” to a four-gamesuspension and a fine equivalent to one week’s salary.77
In addition, the CBA also includes an “Anti-Collusion” clause, whichstipulates that no NFL club shall enter into any agreement with the leagueor any club as to whether to offer a contract to a particular player.78Pursuant to the CBA’s “Anti-Collusion” clause, NFL teams are prohibitedfrom jointly imposing discipline on a player and from creating a blacklist ofplayers with whom the teams collectively choose not to negotiate. ...


Even if one were to presume that protesting during thenational anthem could constitute “conduct detrimental to an NFL club,”there is still a very strong argument that a team could not impose more thana “fine of an amount equal to one week’s salary and/or suspension withoutpay for a period not to exceed four (4) weeks.”82 The CBA explicitly notesthat, in the context of a conflict between language in the CBA and that inthe Standard Player Agreement, it is the CBA language that holdssuperseding weight. ...


If an unsigned NFL player believes that his lack of employmentis due to an agreement among teams not to sign him,87 the player mayattempt to allege a violation of the “Anti-Collusion” clause in the CBA.88At the time of publishing this Article, former NFL quarterback Kaepernickhad just filed a labor grievance against the thirty-two NFL teams, allegingthat his unemployment resulted from collusion among the thirty-two NFL. ...


For Kaepernick or a similarly-situated player to prevail on a laborgrievance of this nature, there would be a need for the grievant to produceactual evidence of an agreement among the NFL teams and not simplyevidence of consciously-parallel behavior.90 Gaining such evidence wouldrequire the grievant to engage in extensive discovery under the CBA’sinternal discovery process.
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