It's also important to notice that it wasn't one-sided. Spock gave as good as he got, with his dry asides about silly, irrational humans and McCoy's hopeless emotionality in particular. One never got the sense that Spock was being picked on for being a Vulcan; he seemed to enjoy the banter as much as McCoy (in his own reserved Vulcan way, of course).
Which is where they got it wrong with Pulaski/Data on TNG, btw. They tried to recreate the Spock/McCoy dynamic with Pulaski and Data, but missed the fact that Data comes as as much more of an innocent than Spock ever did. Data would never think of retaliating in kind, so Pulaski always seemed like she was picking on a defenseless target.