The film, as a historical piece, is presenting the feel and place and time of a certain person, but also shines light on the lives of different sub-populations. When Travis interacts with the other cabbies, it's a theatrical depiction of working class people hanging together. They are the low class, low skill workers and unappreciated veterans; the lower end of the social and economic latter. Then you have these working class people who interact with people they consider "below them" on a daily basis. Their language and behavior towards these others is depicted as permissive and casual in this environment, but also in a low class, working class white environment.
Now there's Betsy and her world. Her world is progressive, youthful, and clearly classier. There is no cursing, the men are depicted as less physical, less gruff, they use their words. She represents the culture of the future, a more caring and empowering culture for men and women.
When Travis takes Betsy out to the theater there worlds clearly clash. Travis's language and behavior turn her off and repulse her. Her lack of acceptance pushes Travis, and what he believes, further into mental isolation. A further sign that while the type of language and behavior may have been appropriate in circles in the past, it isn't appropriate anymore to the socially conscious and sophisticated. The times were seriously changing. The foul language and racism is a sign of class divide in New York and the coming cultural changes. Changes that Travis is not handling well.