First off, I don't watch the NFL. I'm more of a college FB fan (and yes, I know the arguments that college ball is really a professional sport, but that's another argument for another day). Honestly, I don't remember ever seeing the national anthem in the broadcast of a football game. Normally that part of things is pre-empted by the ubiquitous talking heads, and they cut to the field just in time for the kickoff. (Which as an LSU alum, I hate, because the traditional way that LSU takes the field in Death Valley is a spectacle that I miss every time I have to settle for watching the game on TV.) Anyway, I'm utterly amazed that the NFL broadcasts actually include the anthem for each and every game.
So, why do we even play the National Anthem at sporting events where both teams are based in the US? It makes perfect sense at international contests such as the Olympics or the World Cup, where the national anthems are indicative of what country each team is playing for -- a national fight song, as it were. It honestly doesn't seem necessary when everyone in the stadium is the same nationality. It started as a wartime morale-booster in the 7th inning stretch of a baseball game in 1918, and eventually became a customary opening feature during WW2. It's just a custom (one that many people like, true enough, but it really doesn't make a difference to the sport at hand.)
As to the anthem and the flag and "disrepect" thereto... Let's get one thing straight that we all should have learned in 9th grade Civics class. Members of our armed forces do not fight or die for a flag or for a song; they do so for their nation and for a set of guiding principles that define what that nation stands for, not the least of which is freedom of speech. Americans harassing Americans over a mere symbol such as a flag or a song makes a mockery of those principles.
One other thing: as someone who recently saw an armored troop carrier parked outside her neighborhood fire station because of anticipated rioting: this particular protest is as quiet and respectful as any protest movement is every likely to be, and if you know what a riot is like, you should be thankful for that. No one gets tear-gassed, no one is throwing bricks, no one's commute or shopping experience is delayed, children are not being sent home early from school, and not even enjoyment of the sporting event in question is delayed. Not a harsh word is spoken, either. It is silent and it delays nothing. It is being done and getting attention because of the numbers of people who happen to see it happen, so for that reason it's effective: we're talking about it, are we not?