I do think that the depiction of orcs and other humanoids in earlier editions of D&D when it was more obviously influenced by westerns and pulp fiction did have roots in Old West propaganda against native americans.
The earlier editions of D&D are readily available in electronic format. It's not that hard to go directly to the source. That you would raise speculative inferences as to the influences rather than go to the source suggests to me one of two things. Either you are entirely unfamiliar with the early edition material and are speaking out of school. Or you felt the need to cite supporting evidence that backs a racist interpretation of the early edition because you are fully aware how often people can read it and not find any racism present at all. Either way, it's an extremely weak sauce statement.
I use what's actually in the old school D&D books to reliably refute claims of the hobby's "problematic roots." I'm familiar with what the books actually say and specifically where the claims are mistaken or just plain factually wrong.
And I also must chime in in agreement with hedgehobbit's quip:
I know this is a common mistake, but D&D was written in the 1970s, not the 1870s.
I think this has more substance than it seems. Unlike with old school D&D, it's much harder to go back to the original material with old films. John Wayne, of course, starred in far more than his fair share of Westerns. But a lot of his movies just aren't available for a variety of reasons. For instance, his family pulled anything where John Wayne is smoking on screen. There may have been others that have just been sanitizes for modern sensibilities. So unlike with D&D, I can't just say, "Hey, idiot, stop being a mentally obese sack of shit and just go through the original fucking material for Christ's sake!" I do have to resort to making a case via related facts.
And the story as I hear it goes, as we know, in the first half of the 20th century, film was born and bloomed into a massive industry, and there were two world wars. In light of this, at least one of the propaganda agendas at the time was to promote North American unity, and as such there was a concerted effort to show Mexicans and Native Americans in a positive light in the old Westerns. And from what westerns I have seen, they are at least consistent with this thesis.
I do think people who are sloppy thinkers and sloppy at synthesizing knowledge probably get this confused with the popular dime novels of the 1800's where anti-Native propaganda helped the agenda of western expansion of the US, and in particular the building of the railroads. And this is where the bulk of the genocide took place. Government offered land grants to private outfits to get the railroads built. And this is where you get the slaughtering of the buffalo in an attempt to starve out the indigenous peoples. (The American Buffalo, by the way, is the only surviving evolutionary descendent in North America of the large land animals of the ice age--their extinction would have also been a great tragedy perpetrated by the US government.)
Prior to that, there were certainly instances of hostilities between the settlers and the natives. The Plymouth colonists nearly wiped out the Pequots--though it's worth mentioning the colonists had the help of their alliance with the Narragansett and Mohegan tribes. The relations between the white man and the Indians were a lot more nuanced than PC revisionist history would suggest.
So Keep on the Borderlands wasn't influenced by the westerns of the 40s and 50s or by the pulp serials of the 20s, 30s and 40s?
Obviously there's a good amount of pulp era fiction listed in Appendix N as inspirational for the game in general. But can you actually point to anything specific in Keep on the Borderlands that indicates its influenced by Indian genocide propaganda?
There are certain things that jump out at you when you have a good working familiarity with a lot of Gary Gygax's works. One quick thing I'll let you know if you do decide to go back to the original descriptions of orcs and other humanoids and demi-humans, Gary had an obsession with colors. He's very precise and systematic in his descriptions with regard to colors. A less precise, less original author--like a typical gamer--might not be able to create an original race without linking it to their conception of something in the real world. But Gary was not so limited.
There's a colored cave complex in his Isle of the Ape module. I've heard gamers complain that he offers no clues as to what the right path is. I nailed the right path 100% correctly my first time through. Because I understand Gary's obsession with colors.
Gary was also big into play-on-words. And I think "Keep on the Borderlands" was meant to be a play on words. The title is telling you to keep, as in stay, on the borderlands. Because if you bear in mind the underlying assumptions of the game, especially old school, where the idea is some day you would become a king by your own hand, clear your own hex, build your own stronghold, that requires there be vacant land up for grabs. But you still need a civilization to go back to. Trainers to level up. Shops to buy stuff. Bars to recruit mercenaries. If you want to maximize your D&D experience, you should keep on the borderlands. In my opinion, that's exactly what the module is about.