There seems to be a lot of confusion about institutional racism vs. structural racism. There seems to be an argument that protesting during the anthem is not proper because the US Government (for which it's being assumed the flag is a symbol) is not enacting racist practices. While the government isn't taking part in any overt institutional racism (i.e. segregation laws) there is a case, as Landlord points out, that the government has taken part in structural racism, which is where a policy by a governing body substantially effects one group over another.
Another example of this would be the Vietnam War draft boards, which were preferential to educated, wealthy (almost solely white) young men, while those without an opportunity of an education were drafted first. The government wasn't saying "Let's send the poor black kids first" (which would've been institutional racism) but what their policy ended up doing was sending the poor black kids to war first.
I would also like to make the admission that I judge people by their appearances all the time. I try not to let a stranger's race, their clothing, their socioeconomic status, effect how I treat them or think of them, but I would be lying if I said that this didn't effect my thinking. (The goal is to recognize these biases so one can consciously not act on them.) I'd venture to say that anyone who says this is not the case for themselves is naive, and being indignant about the idea that minorities do not suffer as a result of that judgement seems to be where a lot of backlash from this protest is coming from.
I just don't think saying "I'm not racist and none of my friends are racist and the government isn't doing anything racist, also these kids are overreacting" is not made better if you add "...but yeah, racism is a thing. I hope it goes away some day tho."