Near the beginning of the book, Tom Buchanan discusses race.
"Civilization's going to pieces," broke out Tom violently. "I've gotten to be a terrible pessimist about things. Have you read 'The Rise of the Colored Empires' by this man Goddard? This fellow has worked out the whole thing. It's up to us, who are the dominant race, to watch out or these other races will have control of things."
Like today, race in the 1920s was a volatile topic. Because Tom is a disagreeable character, we can interpret Fitzgerald putting these racist words in his mouth as a critique of racism. Yet Tom's fears are relevant, because certain groups in the United States and Europe worry today about the influence of Islamic refugees in the West.
Tom associates Gatsby, whose real name is Gatz, with possibly Jewish origins. Tom is threatened by Gatsby as the possibly non-white other who might invade and take over his civilization. He does his best to exclude Gatsby from his circle of influence, for example by discouraging Gatsby from joining him and his horseback riding friends for dinner. He sneers at Gatsby and his "new" money.