I don't think there is anything to protest: Floyd's killer is going to be tried and very likely punished. I am aware that some people make claims of "systemic racism", "white privilege", and other things very far from the Orthodox mindset. The chief thing to test for that (Does this fit our mindset?) is, "Whose sins am I focusing on here?" and it turns out to be the sins of others. The people talk about racism in the abstract minus concrete examples, and then apply that label and judgement to others on the basis of their skin color. The upshot is that the "SJW" lifts himself up and looks down on others over a sin that (as he imagines) besets them, and not him. He gets into a "holier-than-thou" frame of mind, something quite different from identifying a specific situation and saying that the action is wrong. It is racist, because it judges others on the basis of race, and very often it bears false witness by accusing people in the abstract, many of whom are really not guilty of the imagined, and often imaginary crime.
Abortion is a much greater evil than this, but we do nothing in real terms to stop that, either. If we have any real political power, that should be a greater priority of stopping a greater evil, but we don't. At most, we vote for "pro-life" candidates who later refuse to take real action to abolish abortion for political or personal reasons, and so the same-old same-old goes on, year after year. I don't think Orthodox Christians have any business whatsoever getting involved in even real and genuine peaceful protests - and often they ARE violent affairs manipulated by groups like Antifa and BLM, both of which should be designated terrorist organizations that support violence to achieve their ends and are enemies of what the Church teaches on human sexuality and the family, even setting the spiritual problems of "fighting racism" I mentioned above.
CS Lewis put well the problem of abstract love of distant people who are NOT our neighbor, those near us who we ARE commanded to concern ourselves with:
"Do what you will, there is going to be some benevolence, as well as some malice, in your patient’s soul. The great thing is to direct the malice to his immediate neighbours whom he meets every day and to thrust his benevolence out to the remote circumference, to people he does not know. The malice thus becomes wholly real and the benevolence largely imaginary. There is no good at all in inflaming his hatred of Germans if, at the same time, a promiscuous habit of charity is growing up between him and his mother, his employer, and the man he meets in the train. Think of your man as a series of concentric circles, his will being the innermost, his intellect coming next, and finally his fantasy. You can hardly hope, at once, to exclude from all circles everything that smells of the Enemy: but you must keep on shoving all the virtues outward ‘til they are finally located in the circle of fantasy, and all the desirable qualities inward into the Will. It is only in so far as they reach the Will and are there embodied in habits that the virtues are really fatal to us. (I don’t, of course, mean what the patient mistakes for his Will, the conscious fume and fret of resolutions and clenched teeth, but the real centre, what the Enemy calls the Heart.) All sorts of virtues painted in the fantasy or approved by the intellect or even, in some measure, loved and admired, will not keep a man from Our Father’s house: indeed that they may make him more amusing when he gets there."
"The Screwtape Letters"