Well, this may be because I am one of said white people, but I do agree with RBG to some extent here. I believe in the cause - violence against black people by those in authority is a major issue that needs to be solved, and to do that we need to tackle endemic and persistent racism. It seems like RBG might not be as supportive of Black Lives Matter, although I might be reading too much into her comments.
However, like RBG I see this series of protests as having been highly counter-productive. It has not increased the visibility of the cause, nor convinced anyone that the cause is more in need of attention. It has given the entire Black Lives Matter movement an anti-patriotic flair, though. That is not good for any movement that seeks to attain social change. Social change in the USA comes from within, and there are strong reflexes against any social change proponents who do not appear to love the basis of the country they are seeking to change.
RBG’s comparison to flag burning is particularly apt. I have never seen any advantage to burning the US flag as protest, because that immediately sets that protester as against what the flag represents to the vast majority of people in this country. Refusing to respect the national anthem is having the same effect.
Anecdote time: I live in a mid-range (neither super-liberal nor super-conservative) area of California, and attend high school football games. The crowd there probably skews more on the conservative end naturally, but not significantly so. Every time the National Anthem has been played for the past month or so, someone in the crowd around me (a different someone each time so far as I can tell) has sniped something like “And look: they all stood for the whole thing!” or “Those boys could teach NBA players a thing or two” or similar, to laughter and overwhelming approval. This is in California, where the BLM movement is not a major touchstone but also is fairly well respected. I can only imagine the reactions in areas with more racial unrest or where BLM is not generally accepted as a positive movement.
All of which is to say, I think this particular protest is backfiring, and RBG as usual hit the nail on the head as to why.