Gygax also thought Col. John Milton Chivington had the right of it, so I wouldn't trust his moral judgment.
en.wikipedia.org
en.wikipedia.org
Editing this post - I agree, it could throw suspect on what Gygax's morality regarding Good/Evil/Right/Wrong were...but it doesn't change the assumptions upon why he made level limits and why he tried to make the game humanocentric in AD&D (OD&D on the otherhand, while still humanocentric, had the adage that a player could actually play anything they wanted...I've had players play red Dragons, Horses, Unicorns...etc).
It's hard to make out what Gygax felt about the Sand Creek massacre, but he DID use it to reinforce his ideas of what Lawful Good was (note: It was not the idea that you make peace with everyone or save the women and children, but that a Paladin could actually kill other things...INCLUDING humans if we want to include the Chivington example if Gygax indeed meant to point out Chivington as a Paladin type example).
I've only read the Twitter post, but it appears that the Gygax post there was in relation to alignment, not necessarily race or taking race into consideration. In fact all the examples are pertaining to human on human violence.
It is interesting that he had read (not that it is correct, it may actually be quite wrong) that the Cheyenne Warrior actually backed up Chivington's reasons for the masscre, even though one would have thought the Warrior would have been against it. The Warrior apparantly used the same reasons to slaughter as well. Of course, that comes the paradox of whether that Warrior was Lawful Good either, and if not, if two non-Lawful Good characters can define what a Lawful Good Character actually is.
It's a little off-topic though...as that covers more of what the alignment of Lawful Good actually is and what they can and cannot do rather than addressing race.