Can you change society by changing your preferences?

A map of New York City, where residential areas are colored with dots according to the race of its inhabitants. In finer resolution, each inhabitant is represented by one dot. Non-residential spaces remain white. Image Copyright: 2013, Weldon Cooper Center for Public Service, Rector and Visitors of the University of Virginia (Dustin A. Cable, creator).

Have you ever heard somebody claim to have no negative feelings towards immigrants while living in a neighborhood with hardly any foreigners? What were your initial thoughts? Chances are, they went along the lines of "well, maybe you think you are not racist". Well, maybe you were wrong. 

Are women interested in taking apart desktop computers?

Source: Wikimedia

A very widespread summary of the literature on gender differences in interests (which purports to explain why there are more female nurses and male engineers than vice versa) is that "men are interested in things and women in people". This idea is conveyed in both very serious scientific publications and in the media. This maps well with the stereotype that "boys like to play with trucks and girls with dolls".