Our own American Revolution did away with English monarchy in what became our country, but the government we established took a great deal of inspiration from English Whig politics. In that sense, however radical gaining independence from the English Crown was, our revolution was an American apotheosis of the 1688 Glorious Revolution and a successful repetition of the English Civil War(s) (1642-1651). It was radical, but it wasn't too radical. The French Revolution, though, which drew a good amount of inspiration from our own, was decidedly very radical.
The French Revolution (symbolically begun on July 14, 1789, when the Bastille prison in Paris was stormed by an angry mob) turned the world upside-down. Everything that had previously been regarded as permanent in French society (hereditary privileges and the social/landowning privileges of the Church) was swept aside. This was a turning point in world history; after 1789, there is no going back.
I know that what I've just proposed is a very simple schema of what was a very complex series of historical events; but there is some merit in saying that, without the conspicuous radicality of the French Revolution, there would have been no Marx, no Bolshevik Revolution of 1917, no Sexual Revolution, and (yes) no Black Lives Matter.
The aims of Black Lives Matter are undoubtedly radical, and they do not pretend not to be. Those who most fervently oppose BLM undoubtedly understand this; they stand for the supremacy of law and order over revolution. I am not entirely sure where I stand; I hate complacency with injustice, yet I do not feel myself qualified to make a definitive judgment about the aims of BLM revolution and the viability and wisdom of revolutions in general. One thing I am certain of, though: anyone who celebrates the American Revolution and recognizes, however vaguely, that it could not but inspire the French Revolution, should not be surprised at BLM and its radicality. Revolution is a Pandora's box, and the energy it releases should not be underestimated by anyone, much less those who profess to know history.