However, the Civil War wasn’t one nation invading another. The ‘states’ wanting to secede were official states. Nations don’t require secession. And I’m not sure I get your point “we haven't felt justified in invading other nations to put an end to their grotesque treatment of particular human beings”; Nazi Germany? Was this rhetorical?
Some of them had already seceded, which they felt they had the right to do and regarding which I think they were correct. So they were no longer states of the United States. They were sovereign, or if they had joined the Confederacy they were part of a different nation now. So military forces loyal to the United States, to the extent they remained in Confederate lands past when they were told to leave (and whatever period of time needed for them to leave), were foreign invaders.
My point in that passage that you quoted is that there have been plenty of times when we've chosen not to invade foreign countries to put an end to egregious things that were being done to people in those countries. (I'm not suggesting we always should have, just making the point that we don't necessarily use other nations doing bad things to justify invading them.) There are countless examples. South Africa. Various other nations in Africa. Russia. China. At different points in time various nations have had very nasty #### going on within them. Was the slavery going on in the Confederacy different in a number of ways? Of course it was, so perhaps that kind of interference in the affairs of a foreign nation was justified in that particular case even though such interference hasn't been justified in other cases.
Anyway, Vrai raised the point of evil being subjective. This made me wonder how humans can be so ignorant to their own actions. I can apply to our current generation of progressives that refuse to take responsibility for their own actions; that what they do in harming others or taking from others is justified through blaming others. We justify our ‘evil’. I find it impossible Americans of those days didn’t know it was wrong to enslave other humans. Those same people would have read the Old Testament and Moses freeing the Hebrews from slavery. They have thousands of years of history showing the evils of slavery.
Sure, people have different notions of good and evil though I would hope some consistent principles underlie the distinctions. And at different times and in different cultures have had very different beliefs as to what is evil. Even today there are some that don't think it's evil to - using the power of government and under threat of imprisonment and/or violence - deprive others of the right to choose what to put into their own bodies. Figure that one out.

There are some that don't think it's evil to - again, using the power of government and under threat of imprisonment and/or violence - take money from some in order to give to others. There are some that don't think it's evil to deny people the means by which to defend themselves - whether from other members of society or from the incredible power of government. So, yeah, some people have pretty wacky ideas of what isn't evil or are quite willing to justify evil things as, e.g., being in the best interest of society. (That's all said only slightly tongue-in-cheek.)
I suspect most of the supporters of slavery knew in their guts that it was wrong, that it was vile. But they justified it because they thought it was in their own interests economically or because it helped sooth the discomfort of their own insecurities by facilitating a sense of superiority over others. In their heads they may have been able to convince themselves that it wasn't evil or at least that it was a justifiable evil. But I bet most of them, aware of not, slept less easy because there were still parts of them that knew they were doing grievous wrong.
So I’m still stuck with the question (as an example): If a state or group of states wanted to secede in order to eradicate Jews from their population – whether this be through expelling them or murdering them – do they have a right, under the ‘states rights’ clause, to secede; no matter how evil and illegal their actions?
I think the answer is, rightfully, very much yes. Compare the Articles of Confederation with the Constitution. What is notable in its absence from the latter? Look at the Tenth Amendment. Consider the contexts in which the U.S. Constitution was ratified, and the Union joined, and in particular the temperaments of some of the southern states - e.g., how they felt about ceding more power to a central government. There should be little question that their agreeing to join the Union was predicated on their belief - which is (now) supported by the text of the U.S. Constitution (both what it says and what it does not say) - that they reserved the right to secede from the Union.
That's like saying I'm justified murdering someone even though the law saws I'm not allowed to. Does their rebellion change the fact that they are official states of the United States? This is really a separate issue to secession.
What law are you referring to that said they couldn't secede? That's what is at issue when we're considering whether the U.S. was, at that point, a foreign nation. If they could secede, they were no longer a state in the United States and the United States was a foreign nation.
EDIT: This gets to one of the fundamental differences in the way the United States was formed as compared to so many other nations throughout history. The U.S. was a voluntary coming together of peoples, or states at least. They weren't conquered, they weren't part of the whole - the nation, e.g. - by threat of force. Their lands weren't taken over by one people or another, by one conqueror or another. The U.S. was formed, not taken. It wasn't a rebellion for states to leave, it was just them leaving. Again, they were part of the whole voluntarily. In so much of the rest of the world, and for so much of history, to leave required rebellion (and successful rebellion). That's part of how we were different, we were the great experiment. We changed the rules, we changed the notion of what it meant to be a nation to a great extent. By the nature of the sovereign in our case, as juxtaposed with the nature of the sovereign in so many other historical cases, it wasn't rebellion for a state to reassert its complete sovereignty.
Sadly, for whatever good can be said to have come from the Union's victory in the Civil War, that is part of the bad that came from it. That was lost. We were now part of the whole - part of the nation - by threat of force. That's why so many now, in retrospect, think of what the Confederate states did as rebellion. It was not. But under the notions that control now, based on what our nation is now - because the Union successfully conquered the Confederacy - it is considered rebellion. It would, e.g., be rebellion today for a state to assert its independence. That special character that our nation had, that fundamental difference in how the nation existed and what it meant, was lost with the Civil War. That's just one of the lamentable aspects of it.