#blacklivesmatter racism is a human problem

Yes, a good summary.

I think the focus is good, but alongside all of that one should also have an explanation of the parallel slavery issue. Slavery has always existed, and still exists today, and for millennia people were enslaved without any reference to race. It was just a part of the (usual, more often than not) tripartite division of society, into people who were free/had rights and owned stuff, people who were free/had rights but didn't own stuff (or only very little), and people who were neither free/had rights nor owned stuff (slaves). There have been many variations of this through the ages, but this is the basic pattern. Much of the time, the main ownership that was at issue was of land. Also, if your tribe/whatever lost a war, many of you were going to be enslaved.

By the time modern colonialism happened, there was a resurgence of ethical ideas in the Renaissance, and then in modern thought, that made more people more unhappy about the idea of slavery, which therefore 'needed' a new foundation. As it happened, the people being colonised/enslaved were mostly different shades of brown, so that then you had this idea that they were suitable as slaves because of that, and what that led to may well have been the worst slavery in history.

While Linnaeus is an important source, people like him merely reflected extant prejudice, and disdain for Africans, for example, was also based on Europeans' perceived religious and technological 'superiority' (gunpowder, military organisation--if you conquer them or divide-and-rule them, you can then look down on them irrespective of how advanced culturally they may be). Needless to say, that he provided the connection to 'biology', and therefore the 'scientific' side was an important step, but this wasn't science as such, but the tail wagging the dog.

It's always important to be careful when saying things like 'scientific racism', because even if you provide a decisive rebuttal of it in the same breath, you're still risking the implication that it's 'scientific', when actually it isn't. Just because it was done by a scientist doesn't mean it is or was ever scientific. There was never any method or any scientific acumen in it, same as with later rubbish like 'phrenology' and other absurd claims. Of course, most people understand that perfectly easily, but you always get excessively literal people who will hear the words and assume that because there's a word for it, the concept actually maps onto the world just in the way that it appears in words.

It also has to be emphasised that while it's interesting to trace the usage of the word 'race', of course prejudice against other groups is as old as the hills, and where in later discourse 'race' did a good deal of the heavy lifting when it came to emphasise 'otherness', prior to that there were other ideas that did essentially the same job, like religion, e.g. in pogroms against Jews and Muslims, missions to the 'heathens', etc. I'm not too optimistic that people won't always find something like that, much as even today they continue to pick from the various options that still persist.