Well, yes, but we have to look at the character overall. Sherlock Holmes has his moments against "negroes", but is willing to admit Norbury (a case of an interracial marriage that Holmes completely misinterpreted) is his worst failure, and Watson himself is elated to see the new husband of the white mother willing to accept the mixed race child of her previous marriage. McCoy rails more against Vulcan logic than physiology. It's convenient to call Spock a "green-blooded son of a bitch" but what he really hates is cold logic that makes decisions about life and death without emotion. He'd call a human using the same logic a heartless SOB or worse.
No, to our modern sensibilities it isn't pleasant to hear. But Trek is renowned for making aliens all identical. If Vulcans weren't all ruled by logic, McCoy would be even more at fault for blaming Spock's colder decisions on his heritage. In fact, he's demonstrating faulty reverse logic - all Vulcans are logical. All Vulcans have green blood. Therefore, green blood underpins logical decision making.