My original question was possibly badly-worded. I do not know how to make it better except to post a new question. If I could, I would delete it, but there are now too many answers to do that.
I am not the first to make an objection to this user’s posts: "Cheaper by the dozen" phrase origin? on EL&U actually came about as some sort of response to a “repugnant etymology” (sic) in a comment by the user 271314 on Politics.SE
“forcing prisoners of war to impregnate their mother, resulting in a "dozen" "cheap" children with severe birth defects.”
User 271314 then went on to justify their questionable etymology by posting a heavily-downvoted answer at EL&U.SE which seemed to have little to do with the "Cheaper..." question. (-21, and counting) For some reason, this was awarded the bounty by the OP.
In the “answer” that serves as the supporting argument for the comments which the OP user agc had originally found objectionable, user 271314 manages to convey the idea through their “facts” that African-Americans are inbred, thus continuing the commentary.
Perhaps the question about the origin of the phrase “white races” was a logical jump, but the usage was badly researched, and seems to come from paper-based text. Who on Earth would have a paper-based (or at least PDF) copy of Gobineau’s clearly racist commentary? I edited the quote to remove the excess garbage which had little to with argument. [By the way, each sentence had been laboriously copied by hand, with the little wedgies [>] to make sure all were in block quote.]
In the quote from Gobineau, it is “revealed” that the “white races” are racially superior.
…he claimed that aristocrats were superior to commoners and that they possessed more Aryan genetic traits because of less interbreeding with inferior races.
[EDIT] The question about "first use of the term" white race was actually posted at History.SE about 9 months ago, so the OP was fully aware of the answer. Moreover, they were aware that the first use was long before Gobineau.
Taking the repugnant comments as noted by agc, the overly long and unnecessary implication that African-Americans are inbred, and the blatantly racial and unneeded full publication of the Gobineau paragraph in the question, it becomes obvious that there is a pattern. It is insidious, but pervasive in the user’s posts: all seem to be racially charged for some reason.
>The question is, what is the reason?
As has been noted by Ian Fleming: “'Once is happenstance. Twice is coincidence. Three times is enemy action'”