George Murchison represents an assimilationist ethos in the play. His shoes signal that he has adopted the prevalent values of the dominant culture, as Beneatha puts it, and this notion is indirectly addressed in the dialogue of the scene with the white shoes.
Walter cannot understand the reason behind George's shoes and so mocks them.
Walter: Why all you college boys wear them fairyish-looking white shoes?
Ruth: It's the college style, Walter.
This conversation takes place, notably, after Beneatha has appeared wearing "what a well-dressed Nigerian woman wears" in a robe that Asagai has given her. She has also already explained her views of George as an assimilationist and explained what this means.
"It means someone who is willing to give up his own culture and submerge himself completely in the dominant, and in this case, oppressive culture."
Murchison is proud of his awareness of the cultural nuances of the upper classes. He brags of going to New York and even offers up the factoid that plays start at eight-forty in the evening in New York City, although they start at eight-thirty in Chicago.
When confronted with the claim that he is an assimilationist, George side-steps the accusation and takes a superior line. When Ruth asks for a definition of the term, George says that "assimilationist" is "just a college girl's way of calling people Uncle Toms - but that isn't what it means at all."
One reason George takes this line of reasoning is that he does seem to positively believe that the best way to get ahead is to fall into line with prevailing cultural expectations and take the cultural markers of class as universals. Thus, for George, successful African Americans should act and dress as successful Caucasians do. Successful people act and dress as successful people, regardless of race. (This universalism is a foundational element of assimilationist thinking, especially as it is presented in the play.)
Being a success, to some extent, means having an awareness of the specific etiquette of the upper classes and adopting that etiquette as one's own. If white shoes are the mode or norm for social climbing, socially savvy, upper class college people, then George Murchison will wear white shoes.
Important to note here is the fact that the play leans toward a Pan-Africanism at times by portraying Asagai in a generally positive light and by showing Beneatha's preference for Asagai as well. However, the play does not make any ultimate or final declarations as to whether or not assimilation and integration are adequate solutions to America's race problems. George, for all his arrogance and shallowness, may be on the right side of the debate. After all, he is the richest person Beneatha knows (or has dated) and has a strong sense of his own future. He may be lacking soul, in some ways, where Asagai does not, but the politics George represents are not entirely cast into doubt.