Overall, the characters in The Great Gatsby scream "WASP"-ish behavior, both in physical appearance and in their judgment of others. Every major character is white and presumably Protestant. The attitudes of two characters in particular, Tom Buchanan and Nick Carraway, reflect general attitudes during the Roaring Twenties. Therefore, it is not a far stretch to believe that the events of the novel occur in 1922.
One of the most memorable moments of racism is at the Buchanans' dinner table, when Tom, during "normal" dinner conversation, mentions:
It's up to us who are the dominant race to watch out or these other races will have control of things...[t]his idea is that we're Nordics. I am and you are and you are and -- and we've produced all the things that go to make civilization -- oh, science and art and all that. Do you see? (17-8)
Most of my students identify Tom as the most obviously racist character in the novel, often using this statement alone as evidence. Nick, however, also has his prejudices:
As we crossed Blackwells Island a limousine passed us, driven by a white chauffeur, in which sat three modish Negroes, two bucks and a girl. I laughed aloud as the yolks of their eyeballs rolled toward us in haughty rivalry. (73)
Reading in context, we can see that Nick suddenly adopts a judgmental and somewhat sarcastic tone. Certain words and phrases ("modish" used sarcastically, "bucks," "haughty rivalry") give us clues that Nick is expressing his distaste here. In no other place in the novel, for example, does Nick use the word "buck" to describe another male; his use of the word here insinuates that he equates African-Americans with animals.
Nick also reserves stereotypical judgment for the "Jew" Meyer Wolfshiem. Here, Nick uses "Jew" more as a cultural descriptor than as a religious reference, but he still uses words that express distaste for Wolfsheim's cultural background as well as his overall personality. For instance, Nick immediately describes Wolfsheim's nose. Sadly, many of my students remember Meyer Wolfsheim simply by the beginning of Nick's description of the man as a "small, flat-nosed Jew" (73) (though in jokes of poor taste, Jews supposedly have large noses). Later, Nick again describes Wolfsheim's nose: "His nostrils turned to me in an interested way...." (75). Nick makes assumptions about Wolfsheim based on appearance alone -- even before he begins talking to him.
Finally, though we might describe most of the characters in The Great Gatsby as typical white, Anglo-Saxon Protestants, their lives are full of decadence, not overtly religious zeal. Characters party and drink. By the end of the novel, Nick describes Tom and Daisy in particular as:
...careless people...they smashed up things and creatures and then retreated back into their money or their vast carelessness or whatever it was that kept them together, and let other people clean up the mess they had made....(188).
When Catherine spreads the rumor that Daisy and Tom will not get a divorce because they are Catholic, Nick denies the rumor, but does not attack the Catholic faith (38), unlike some earlier comments characters made about those who are "different."
Overall, most of the characters in The Great Gatsby view race and religion as non-negotiable. The "white is right" mentality certainly permeates the novel, though some characters are more judgmental than others.