I agree with your point, but I think it's not fair to blame cultural relativism. Relativism means not prescribing a single morality applicable in all contexts. That's something on which reasonable people will differ. If you do accept it though, you're not obliged to permit everything.
For example I think that there were relatively moral people who lived in e.g. the US and Saudi Arabia ~300 years ago and accepted slavery unquestioningly. It would have been better if they had questioned and rejected it, but I don't think they are evil for not doing so. In the modern US I think that only someone tremendously immoral would accept and participate in enslaving others.
This belief makes me a moral relativist (at least by some reasonable definitions). All the same I think I'm much closer aligned with your feelings on the morality of modern Middle Eastern society than GP.
All that to say, being a moral relativist allows you to have weird dissonant views, but it doesn't require it.
Slavery, throughout history, was generally not seen as desirable. Rather, it was either seen as a necessary evil, upon which a "logical rationale" (read: cognitive dissonance) was built up to justify it, or as a form of punishment. Aristotle actually predicted its end about 2000 years before it happened [1]:
---
For if every instrument could accomplish its own work, obeying or anticipating the will of others, like the statues of Daedalus, or the tripods of Hephaestus, which, says the poet, "of their own accord entered the assembly of the Gods."
If, in like manner, the shuttle would weave and the plectrum touch the lyre without a hand to guide them, chief workmen would not want servants, nor masters slaves.
- Aristotle ~350BC
---
He also made regular indirect mention of abolitionists and abolitionist causes, which have obviously existed for millennia. It's not just some coincidence that the Industrial Revolution happens and within about a century most of every country (that had benefited from said industrialization) had outlawed slavery. It's not that we became more moral, but rather it became comfortable enough to dispose with slavery. So we did, and then attributed that to "modern thinking."
That is an immense leap from "if we could have machines do it, we wouldn't have slaves do it" to seeing slavery as undesirable. Aristotle was a staunch believer in "natural slaves" who didn't have the faculty of rational deliberation and therefore were (and should be) guided by those who do have that faculty.
This line of thought can be traced all the way through to the modern day, and obviously well up to abolition.
There's really not much evidence at all that slaveholders saw their activities the way you describe ("necessary evil"). There's no evidence that we first had a necessity for slavery and then obviated it through automation. In fact, automation in the Americas increased demand on the labor of enslaved people.
If there was any external triggering event of abolition, it'd have been Darwin's On The Origin of Species and contemporaneous breakthroughs in science that destroyed the philosophical foundations that slavery was built upon (natural god-given supremacy, as Aristotle believed).
The abolitionist movement was an intellectual and moral one, through and through. You can just read the writings of abolitionists to hear what convinced them into their positions.
Wiki has a reasonable listing of the countless times slavery was abolished throughout history. [1] That list should be considered extremely incomplete, as it happened with quite the regularity, all around the globe. And so even calling something "the" abolitionist movement is a misnomer. Abolitionist movements, political leaders, and abolitionary successes have existed for thousands of years, and likely for as long as slavery itself has existed.
But it never remained abolished because of a simple logical problem you run into. The reality of the world - past, present, and future - is that stronger powers dominate weaker powers -- the same reality upon which Aristotle based his cognitive dissonance. And so so long as slavery provided a significant material benefit, powers that embraced slavery would dominate those that did not. And that dominance would inevitably lead to the institution (or reinstitution) of slavery in the weaker powers. The British Empire and its spread of slavery around the globe is but one of many examples.
So you saw this regular flip flopping. One ideologically minded leader would end slavery, only for it to come back later. What changed with the industrial revolution is that the latest end of slavery no longer had any particularly negative consequences, instead we saw the exact opposite. Countries that abolished slavery, which was primarily a rural/plantation based phenomena, actually started to grow exceptionally rapidly on the back of the emerging systems of industrial wage labor, while rural and plantation style production became less and less economically relevant. Slavery had become obsolete.
---
There's some interesting parallels with slavery and modern day conscriptions. A country locks up its borders, prevents people from leaving, starts forcibly conscripting them into the military, gives them a gun, and sends them off to die. This is utterly barbaric, and most people would agree with such. Yet it remains a thing, and will remain a thing for the foreseeable future, for the exact same reason that slavery was perpetuated.
Countries that turn to conscription will be more powerful than those that don't. When this reality becomes no longer true (perhaps due to war becoming more mechanical in nature) we'll certainly finally abolish this barbaric behavior, and then claim it's due to some 'greater moral understanding', as if people alive today can't see with their own two eyes what an unnatural and abhorrent behavior this is. Of course we can! But trying to permanently stop something that's a significant means to power is like trying to stop a train by walking in front of it.
Sure, I don’t believe cultural relativism is itself in all cases wrong. I think it’s obviously wrong when used to excuse obviously immoral things done in a context where they are in fact obviously immoral (such as much of the Middle East in the modern day).
For example I think that there were relatively moral people who lived in e.g. the US and Saudi Arabia ~300 years ago and accepted slavery unquestioningly. It would have been better if they had questioned and rejected it, but I don't think they are evil for not doing so. In the modern US I think that only someone tremendously immoral would accept and participate in enslaving others.
This belief makes me a moral relativist (at least by some reasonable definitions). All the same I think I'm much closer aligned with your feelings on the morality of modern Middle Eastern society than GP.
All that to say, being a moral relativist allows you to have weird dissonant views, but it doesn't require it.