"You're white, all right" definitely refers to the Virginian's race (as its context makes rather clear). According to commentaries I have seen so far about this work, the Virginian is of Anglo-Saxon heritage, and readers are to understand at face value that he is unquestionably white. I think that may explain his cool attitude in response to the "compliment": it's pointing out the obvious, and so is not really a "high compliment" at all because it could go without saying. Also, the man saying this is a salesman who can be assumed to have the motive of "buttering up" the Virginian to try to sell his product: even legitimately complimentary words from such a source would be of questionable sincerity. Compare what the narrator says a little later when another salesman uses the phrase "old man":
The drummer had struck a slightly false note in these last remarks. He should not have said “old man.” Until this I had thought him merely an amiable person who wished to do a favor. But “old man” came in wrong. It had a hateful taint of his profession; the being too soon with everybody, the celluloid good-fellowship that passes for ivory with nine in ten of the city crowd. But not so with the sons of the sagebrush. They live nearer nature, and they know better.
Providing more context to this interesting question seems to require a rather complex understanding of various prejudices that Wister held. While I suspect I am not up to the task of fully answering it, here are some things I found that seemed relevant:
Wister believed in the superiority of the "Anglo-Saxon"
Wister was unquestionably prejudiced and, more specifically, believed in "Anglo-Saxon" supremacy over other races (in the broad sense, including other European races). "Owen Wister's Paladin of the Plains: The Virginian as a Cultural Hero", by David A. Smith, includes the following quotation from Wister:
... requires spirit of adventure, courage, and self-sufficiency; you will not find many Poles or Huns or Russian Jews in that district; it stands as yet untainted by the benevolence of Baron Hirsch. Even in the cattle country the respectable Swedes settle chiefly to farming, and are seldom horsemen. The community of which the aristocrat appropriately made one speaks English. The Frenchman today is seen at his best inside a house; he can paint and he can play comedy, but he seldom climbs a new mountain. The Italian has forgotten Columbus and sells fruit. Among the Spaniards and the Portuguese no Cortez or Magellan is found today. Except in Prussia the Teuton is too often a tame, slippered animal, with his pedantic mind swaddled in a dressing-gown. But the Anglo-Saxon is still forever homesick for out-of-doors.
"Unseemly Realities in Owen Wister's Western/American Myth" (Sanford E. Marovitz, American Literary Realism, 1870-1910, Vol. 17, No. 2 (Autumn, 1984)) seems to provide a more detailed exploration of Wister's racial prejudices and how they affected his work; but I haven't read it (fully) yet.
The one giving the "compliment" is a Jewish peddler
In light of the above, the racial composition of the parties conversing in your question seems relevant. The Virginian is conversing with drummers (old-fashioned slang for salesmen/peddlers) who are described as
“Two Jews handling cigars, one American with consumption killer, and a Dutchman with jew'lry.”
The one speaking with The Virginian is apparently one of the two Jews:
“I can tell a man when he's white, put him at Ikey's or out loose here in the sage-brush.” And he rolled a cigar across to the Virginian's plate.
He does not seem to be portrayed positively by the narrator, who wonders
if he had attained that high perfection when a man believes his own lies.
Marovitz also understands the depiction of the Jewish drummers as negative:
Apart from a quick derogatory description of two Jewish drummers early in THE VIRGINIAN-where they are treated, however, no more harshly than other traveling salesmen briefly portrayed-there is no overt racial or ethnic prejudice evident in that novel
(I'm not sure the second half of that sentence is correct...)
My interpretation of this passage is that the labeling of "you're white, all right" as a "high compliment" is indeed meant to be ironic. I'd be surprised if it is not a reference to race, along the lines of "mighty white of you" or "play the white man". While on the surface of it this is a "compliment", I think what's going on is that the Virginian is not thrilled to be told the obvious (that he is white) by someone who I get the sense he would have looked down on as a social inferior. So my read is that it's not that being white isn't considered something positive by the Virginian or the narration, but that it is beneath him to be proud of simply being told "You're white, all right." Also, as a man of Anglo-Saxon heritage, he may possibly reject the Jewish salesman's implication that they are both racial equals belonging to the overarching category of "white men" (if we are meant to understand the drummer as asserting that status for himself).
Through Google, I also found the following view on the function of this scene. Even though the drummer who says the line does not seem to be portrayed positively, his testimony that the Virginian is "white, all right" might be a way of conveying this information to the reader:
When racial diversity appears in The Virginian, it is mostly in order to affirm white superiority. The Virginian's whiteness plays an important role in one of the opening scenes of the book, where he encounters a peddler (over a meal) whose sole function in the text seems to be to provide testimony to the Virginian's racial purity.
("Manly Cooking, Ideal Masculinity", in A Taste of Power: Food and American Identities, by Katharina Vester, page 82)
To sum up:
- Yes, the comment is related to race.
- Being white is understood to be positive, and so simplistically can be seen as a compliment (and some expressions in historical use seem to have used it as such); however, I think it's likely that the Virginian did not find it meaningful to receive this "compliment" in this context from this speaker, so the description of it as a "high compliment" is ironic, not sincere.