Yes the NFL is in quite a bind. Alienate its audience or a group of its players.
Thing is I have sympathy for the issues CK claims to be concerned with but
1) He does this causes more harm than good
2) I don't believe this is anything more than a self absorbed tantrum by a player on decline facing being booted on his but and I find it no coincidence he spoke out hours after Fox Sports called for the 49rs to cut him for his bad play.
I actually hate the national anthem, I think it is horrible and America the Beautiful should have been chosen not this in 1931. I didn't know about this verse but it is bad.
As far as Blacks being given a hard time by the police, yea that is 100% accurate. Anyone who thinks it is not is a fool. So what do we do about it? What does BLM suggest? I do know that chaining yourself to highways etc... hurts your cause. By the way this being done in Boston was a coordinated with a legal group who were probably hoping that the police would overreact, infringing on civil rights and allow for a big fat $ lawsuit. The Westboro Baptist church (run by lawyers BTW) has a similar business model.
You can't legislate what people feel, only actions and although not perfect, police body cams are the best shot we all have of accountability from the police. It also protects the police from false claims. This is an issue for all Americans. I look like the last person on earth who the police would give a hard time to but I like almost everyone I know have a couple bad police stories for things abusive police did to me. I like the police 99% of the time and don't let the two bad occasions I have had have me label all police. My sister, in a minivan with two young children in it turned around in a driveway in a town near Gillette and the State trooper (woman) who lived there and was in the house (unknown to mys sister who was just turning around) rushed her with gun drawn. Think about that, a Massachusetts State Police woman pulled a gun on a woman in a minivan with two small children just for turning around in her driveway (yes this is what the trooper was screaming about with gun pointed at my sister). Luckily my sister didn't panic or she could have been shot for trying to" run down a policeman". This state trooper is a well known hothead, a hothead with the power to kill yet she is still on the force.
Back to CK. I think he is self absorbed and has used this as a way to get support and play the victim card to cover that he is a bad QB and going to get cut. I hate that.
I think the NFL does nothing and the best we will see is CK cut for his bad play as he should be.
edit: FYI story on how Westboro Baptist Church funds
How Westboro Baptist Church Makes Its Money