The league has full authority over what happens on the field of play, and full control over what the players may or may not wear on the field. I’m sure the national anthem conduct will be covered in the next agreement, since it apparently is not mentioned at all in the current one.
One would certainly hope so. Let's define "field of play" by reference to the fact that at one time a player who ran out of the end zone and spiked the ball or threw it into the stands after the play could be fined; i.e. behavior outside the white lines such as kneeling at the sideline as we see with the protests.
Which leads me to question as you suggested upthread that "every lawyer that has looked at it", says the league cannot take disciplinary action. Unless, of course, such provisions have been negotiated away (and why would they have been?)