In Mary Shelley’s Frankenstein, Frankenstein’s monster weeps upon hearing about how Native Americans were treated. Was this a common sentiment for Europeans in the late 18th and early 19th centuries?

In short, yes.

And no.

Actually, it's complicated.

First, the most basic question: which edition of Frankenstein? The 1818 version (which is more science-horror) or the 1831 (which is the one most people read, and is more religiously-minded)? I think I remember this passage from the last time I read the 1818 version... but I'm not sure.

Either way, you can approach the question of whether Europeans from the 1750s to 1850s expressed concern, emotions of regret or pain, or even outrage from a number of different directions.

The Literary Angle.

Shelleys work is a work of early Romanticism. The Romantics (which included Shelley's husband Percy) were all about using their literary craft to excite emotion or generate passionate feelings. That's why, in Mary's Frankenstein, there's so much anguish: Victor tearing at his breast, Victor falling down and weeping, Victor swept up in the powerful scenery of the mountains he's climbing, Victor recoiling in abject horror, etc. etc. Coming out of the more cerebral Enlightenment, the Romantics were all about feeling.

And one of the ways to evoke this feeling was to tap into older tropes about the misery of human history--tropes of lament that go back before the early Christians, even, to the great literary figures of Classical Rome. Tacitus' Germania was in some ways a pointed critique to Romans of their own political and moral corruption of course, but it was also a lament for these sturdy, simple German people, who were doomed to be conquered by Rome, and assimilated by them. (as Rome had done to so many other peoples.)

(Christopher Krebs has a good book out on Tacitus--A Most Dangerous Book (2011)-- where he writes about the Germani as one of the first groups to be seen as "noble savages"... who were doomed by the wheels of history to fall under the expanding yoke of mighty Rome.)

Interestingly, though Bartolomeo de las Casas, who wrote passionately about the destruction of the Indians (by Spanish rule in Latin America) in the 1540s, is often described in history survey classes as a pioneer humanitarian and even a cultural relativist--because he not only cared about the Indians, but wrote respectfully of their ways and tried to argue that their ways were something other than 'savagery'--he was actually on pretty solid and well-trodden ground literarily, as there had existed this 1,500 year-old genre of lament for the defeated, pity for the fallen, regret for the destruction of the noble-savage foe.

In Shelley's Frankenstein, when the Creature reads, he/it reads a bunch of 18th century, Romanticism-tinged histories... including Volney's Ruins of Empire (a lost classic) written in the 1790s, describing the fall of civilizations of the past. This late 18th century history in turn was drawing on 2,000 years of classical lament for the defeated, the disappearing, and the dying.

Shelley was very well-read. By including this wide range of literary and historical works in Frankenstein, she was of course flexing her intellect. But she was also digesting these books for a more popular audience. She's sort of a fusion of Carl Sagan and Stephen King... but I digress.

So, how many readers in (say) 1830s London, as they read about the monster in tears over the fate of the Native Americans, shared the feeling? Difficult to say. Certainly some. It would not have felt "strange" to read the words, because it was an established literary motif, both for the Americas (from Las Casas onwards) and for all suffering "noble savages" everywhere. (more on that below.)

The American angle.

This is the one that I'm not qualified to really grapple with (because my American history is so weak). Nonetheless, while the most recent trend in American historiography has been to emphasize how the eradication/removal of Native Americans amounted to a genocide (with genocidal policies but also genocidal motivations), an older generation of history emphasized the "deep regret" with which American political leaders, religious leaders, thinkers and writers, and even soldiers and journalists confronted or grappled with the way that European Colonials/the Early United States pioneers brutally treated the Native Americans. From Henry David Thorough to (maybe?) Laura Engles Wilder. But I don't know enough to say more on this however.

Regardless, I doubt Mary Shelley would have been very tuned in to this discourse. It's too early in the century.

First off, she would not have been that up on American culture or events (though Wikipedia tells me she met Aaron Burr... I did not know that!)
But she would not have been reading American books for sure... because no one was, since the United States was such a political, economic, and cultural backwater. A cultural wasteland, if you will. Not worth the time. (and has this really changed....? but I digress... :-)

Alexis de Tocqueville's influential book on America, which did regret the treatment of Native Americans (though I read this decades ago, so take with a grain of salt) wouldn't be published until the 1830s... well after the second edition of Frankenstein. So Shelley couldn't have read it, and probably wasn't very aware of early (early 19th c. United States) disagreements on the cruelties of "Indian Policy."

The Imperialism angle.

But even the literary tropes of regret, lament, and compassion for the suffering noble savage mentioned above could have various implications and various things "feeding" into it.

In the escalation of imperialism that first began stirring (or rather, reviving) around 1815 and peaked in the 1880s & 1890s, there was a growing fascination with--even obsession with--the "dying" or "vanishing" races of primitives. One of the key books here is Patrick Brantlinger's Dark Vanishings: Discourse on the Extinction of Primitive Races (2003), which is worth a read (though I think he's a literary scholar, not a historian??).

Either way, there was a lot of ink spilled by scientists, explorers, missionaries, politicians, poets, and journalists about how the "primitive" peoples were doomed to disappear after contact with "civilized" races. Brantlinger calls this "extinction discourse"... which he sees as an offshoot of imperialist and racist discourses, in that--despite their tone of lament and regret (and in some cases call for efforts at "preservation")--presented this physical/cultural/historical eradication as inevitable... and thus became a sort of self-fulfilling prophecy.

Obviously, Charles Darwin is a key figure here. In his section on “the extinction of races” in The Descent of Man (1871) Darwin writes,

When civilised nations come into contact with barbarians the struggle is short, except where a deadly climate gives its aid to the native race.

But Brantlinger's work shows how this theme--of primitive races being doomed--predates Darwin significantly. (In fact, the more I learn about Darwin, who published the Origin of Species in 1859, the more I see how he really compiled long-standing ideas, observations, and tropes rather than originating them .. but I guess that is always the case in history, there is nothing new under the sun.)

Anyway, while Darwin's work on "extinctions" of human groups in 1870s was a half-century after Shelley wrote Frankenstein, Brantlinger shows how much this idea was in circulation much earlier, even around 1800... which the erudite Shelley would have absorbed.

And, to repeat: while this notion of the regrettable dislocation of, vanishing of, death of "primitives" (the new "noble savage") was often one that made people feel sympathetic or even sad, it could also be deployed as one more element in the ideological arsenal of empire:

"The primitive civilizations are doomed! This means there is no reason not to annex this island/sell this rum/beat back this savagery with volley fire...!"

"No, sir, I disagree! Yes, the primitive civilizations are doomed... but this means that we have the moral obligation to go in and protect them, to minimize the damage, to administer their transition to civilization, to make sure it is done correctly!"

"Good Sirs, I could not disagree with you both more! Yes, the primitive civilizations are doomed... and so we must fund a Great Museum, in which we will place on display all of the objects and artefacts collected from the primitive peoples, so at least some elements of their primitive culture will be Preserved for All Time!"

All of these themes actually work equally well with imperial expansion.

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