If the NFL Commissioner, Owners and Coaches want to be neutral then the proper way to handle this would be going back to rules prior to 2009 when players did not take the field until after the National Anthem. Do that, along with issuing a statement that they're in the business of playing football, that they and the players will not use game day to make political statements of any kind. Simple. Well, the purists, both left and right wouldn't be happy, but they are in the minority. A loud and vocal minority, but a minority none the less.
Had they done this day one, it's a long gone issue. Now it may be too late to do anything to eliminate the problem. people are dug in on all sides.
Actually prior to 2009 nearly all the NFL teams at all the games took the field for the national anthem. The rules in 2009 simply made it mandatory.