Do NFL players have the right to protest, specifically while "on the job"? That's arguably determined by their employee contracts, not by the First Amendment or a tweet from Donald Trump. Was their protest today reasonable? That depends, I think, on what their protest was premised upon. Two of the most frequently-cited reasons are: (1) To denounce Trump's recent inane remarks, and (2) To draw attention not to police misconduct, per se, but particularly to police mistreatment of our African-American community.
I think Reason 1 is perfectly reasonable, as I support most peaceful efforts to defy Trump and expose his buffoonery. Reason 2 is predicated on an empirical assumption: that African-Americans are, in fact, systematically mistreated by law enforcement. Is this factually correct (even when, say, controlling for economics)? To be clear, this question cannot be satisfactorily answered by citing news stories of such mistreatment. What does empirical research have to say?
The research I looked at (and I am admittedly not an expert in this field) concluded that, while blacks are more likely be "roughed up" by cops, they aren't more likely to be gunned down than whites. As I've said, however, the story of an unarmed, law-abiding person of color who was murdered by a cop is far more newsworthy than one who wasn't, and there are enough active cops in this country to ensure that such stories will be reported on a seemingly daily basis. I will never exploit blacks by extrapolating from these tragic, yet extraordinary stories in order to advance my anti-Trump agenda or feel good about myself, and that's exactly what I'd do if I ignored such research. Now, if protests centered on apparent racial disparities in, say, the handing out of death sentences, then I'm all on board.
In short, my feelings are mixed on this one.