In hindsight, when Donald Trump was telling Dallas Cowboys owner Jerry Jones (it is my understanding that they had a conversation about this issue before Jones' controversial public statements) to take a firm stance against the anthem protests, I don't think Trump understood the trouble he would be bringing to Jones and other owners. There are actually many different angles by which to launch a lawsuit or complaint regarding Jones' stance. Here are some:
(1) An owner, such as the owner of the Houston Texans Bob McNair, makes a stupid remark comparing football players to "inmates." New protests are triggered over what's perceived as racially condescending attitudes to the athletes by team owners. Punishing the players now will bring an expensive discrimination/retaliation lawsuit.
(2) Perhaps some Black or minority players feel there is discrimination of some sort that the NFL has not addressed, such as disparate treatment with disciplining, bullying, representation among coaches, etc. Whether or not this actually exists is beside the point -- a good-faith belief alone is a serious matter.
(3) Perhaps a player may kneel down as a religious protest against war or a specific foreign policy that he feels is contrary to his religion. It's a fact that on many occasions in history there has been conflict between religious ideals or practices and nationalistic aims.
(4) Players may join hands and kneel in solidarity during the anthem because they feel they bear some responsibility to send a positive message to society with what influence they have. They may believe that their behavior on the field will impact them both on and off the field, as human beings. This would arguably be covered by the National Labor Relations Act as "protected concerted activity."
These are just some ideas off the top of my head. Point three above would clearly be a constitutional matter, in my view. There are so many references in the Bible and other religious texts against war or harming your fellow man. While I'm not particularly religious and may not agree as to the effectiveness of this type of protest, I can see an NFL athlete using this argument to draw attention to a matter of religious significance. Some religious people eschew nationalism as a distraction to spiritual aims. Possibly a judge or panel would reject this argument and assert such a protest is not religious in nature, but I think it could go either way, and at minimum bring financial loss and embarrassment to the respondent.