It really boils down to a few simple facts:
1. As with any business, are you as the owner going to allow the employees to dictate the way the business is run?
2. The NFL is in the entertainment industry and the fans have overwhelmingly demonstrated that they do not want politics or personal grievances injected into the game.
Personally, I love winning, but I'd rather lose with players that represent my values than win with a bunch of thugs and criminals.
You can say the same thing about Hollywood but they survive.