Obviously it's a political statement. I'm not saying that it isn't, or that it is recognised as such. What I'm suggesting is, this itself is the source of the outrage. The sort of patriotic ritual represented by the flag-and-singalong are assumed to be apolitical, assumed to assert generally American virtues which are beyond dispute. Kaepernick's protest isn't distressing simply because they disagree with the politics it espouses, but because it is explicitly political, because it recasts the whole ritual as a political one- which, of course, it always was. If the same point had been in a context that was recongised as political, such as a BLM protest, the anti-Kaepernick crowd may disagreed with him, even vehemently, but he wouldn't have risked the same sort of bile, because he was not violating a sacred myth that the rituals of nationalism are somehow apolitical. It would have been a passing item on the sports blogs, "up and coming quarterback attends protest", and NFL-ignorants like you and me would still think that "Kaepernick" refers to a style of Lithuanian pickled gherkin.
The fact that his protest consisted of nothing more than an act of passive refusal- that his outrage consisted of literally keeping his head down- only serves to hammer home this point. Kaepernick didn't need to actually say anything disrespectful to "dismiss the entirety of American history and culture as immoral". All he had was fail to practice the expected affirm of American nationalism that was expected of him as a football player, and the reactionary right would fill in the blanks. Anything less than unquestioning compliance was tantamount to treason...