In The Great Gatsby, how is this quote significant to the plot? "The idea is if we don't look out, the white race . . . . it's been proven."

The quote in context is as follows:

Civilization's going to pieces . . . I've gotten to be a terrible pessimist about things. Have you read "The Rise of the Coloured Empires" by this man Goddard? . . . Well, it's a fine book and everybody out to read it. The idea is if we don't look out the white race will be--will be utterly submerged. It's all scientific stuff; it's been proved.

The passage is more significant in terms of character development rather than plot. It is Tom Buchanan who makes this racist statement early in the novel when Nick goes over to the Buchanans for dinner. He is talking about a book he has been reading, The Rise of the Coloured Empires. Daisy observes: "Tom's getting very profound . . . . He reads deep books with long words in them." This seems to be new behavior for the former football player whose glory days are behind him. Even though Daisy makes casual fun of Tom's passion in discussing the new half-baked social theories he has discovered, Tom continues in more detail, which impresses Nick in an unexpected way:

There was something pathetic in his concentration as if his complacency, more acute than of old, was not enough to him any more.

Thus, the passage itself is not significant: The fact that Tom Buchanan has read a book is significant, which reveals a great deal about his character. Nick muses over this fact as he drives home after the oddly illuminating dinner:

As for Tom the fact that he "had some woman in New York" was really less surprising than that he had been depressed by a book. Something was making him nibble at the edge of stale ideas as if his sturdy physical egotism no longer nourished his peremptory heart. 

Despite his life of wealth and privilege, Tom Buchanan is clearly dissatisfied and restless.