I don't recall any significant role of Jimmy's wife in 'Pulp Fiction'. Maybe she is just part of Jimmy's background story that isn't explored much in the movie.
In 'Pulp Fiction', Jimmy's wife is named Bonnie. She is a character that, although not in the thick of the main action, has a significant impact on the story. When Vincent and Jules end up at Jimmy's place with a rather messy situation in their car, Bonnie's expected arrival home soon forces them to take quick and somewhat comical actions to clean up and get out of there without getting caught by her.
Well, Jimmy in 'Pulp Fiction' is a character who plays an important role. He's a friend or acquaintance of some of the main characters. His house is a significant location in the movie at one point. He has to deal with the presence of some rather dangerous and unpredictable people in his home, which creates a lot of tension and some comical moments too. He's basically a normal person thrust into extraordinary and often dangerous circumstances that are typical of the 'Pulp Fiction' world.
In 'Pulp Fiction', Jimmy is that character who has this sort of regular - joe - caught - in - the - middle - of - mayhem feel to him. He's not part of the main criminal underworld like Jules and Vincent in the purest sense, but his connection to them drags him into their wild situations. For example, when they need a place to clean up and hide out for a bit, they turn to Jimmy's place, which causes all kinds of tension and comical - yet - dangerous moments.
Jimmy was a guy whose house was used as a hideout or a place for the characters to deal with certain situations. His presence added an element of complication to the plot.
In my view, Jimmy isn't racist in Pulp Fiction. His character seems more focused on other issues and his interactions don't show any discriminatory tendencies based on race.
Jimmy is sort of an incidental character. He's got his own life going on until these unexpected visitors disrupt it. His place becomes a temporary refuge for the protagonists.