Why is McCoy so Racist Within an Otherwise Accommodating Universe?

Question

Based on a thought I had reading through some answers to this question, and many sentiments I've heard over the years about Gene Roddenberry's vision for a universe of total racial acceptance, cultural diversity, etc, why does McCoy always seem like such a flippin' racist toward Mr Spock?

I get that Kirk had a categorical mistrust of Klingons because a Klingon murdered his son, so—okay—he had an emotionally charged reason behind what he said in STVI which blinded him temporarily. Does McCoy have something in has past like this? Is he just a crusty old Southern fossil? Is racism toward other species accepted with the general idea among humanity that they're only down with tolerance among other Earthlings? What's the explanation for McCoy's attitude

Answer 1

Yes, he is a crusty old Southern fossil.

The official Star Trek database (at StarTrek.com) uses your choice of words, almost verbatim, in describing McCoy's disposition:

His temperament was sometimes argumentative, a cynic's outer crustiness masking deep caring beneath the surface. His "old South" roots led to the old-time physician manner of doctoring, with a Southern accent that was most apparent when under stress....McCoy played his role as psychologist expertly to the hilt — especially for the ship's two senior officers. As such an emotional watchdog he was not afraid to take on his captain, but it was his running battle of wits with Spock which became legendary. Spock showed his true feelings, though, as when inviting McCoy down to Vulcan for his "wedding" and in storing his katra with him before a known suicidal saving of their ship before the Genesis detonation.

(Source)

In other words, McCoy and Spock have an underlying respect for one another, but McCoy displays a kind of biting wit and "crustiness" that mask his respect for Spock.

All in all, while humanity has evolved by McCoy's time to have eliminated most public displays of prejudice, this does not mean that every single individual adheres to this, and certainly not in equal measures.

Even by the 24th Century, humanity still has an underlying strain of prejudice. From "Encounter at Farpoint":

RIKER: But your files, they say you're a —

DATA: Machine? Correct, sir. Does that trouble you?

RIKER: To be honest, yes, a little.

DATA: Understood, sir. Prejudice is very human.

Answer 2

In dramatic terms, McCoy can get away with being so irascible because he is the ship's medical officer. His devotion to the well-being of the crew (including Spock) provides a balance to his crusty exterior. The same balance would not work, for instance, in a science or weapons officer.