Industrialism is not central to the plot of The Importance of Being Earnest by Oscar Wilde. The Industrial Revolution is reflected most clearly in the play in the presence of the railway. Although aristocrats in earlier centuries tended to gather in London for the "season" and the retreat to country houses in the summer, railroads are the enabling technology for Jack's rapid movements from city to country.
The Miss Prism subplot also relies on technology. First, of course, the infant Jack was left by accident in a handbag at Victoria Station. Next, the sort of novel she is described as writing is associated with "railway stalls," which sold cheap popular novels (often on themes of romance or crime). In Wilde's time, they were disparaged as lowbrow fiction and criticized as exemplars and causes of cultural decline.
Another common trope found in the novel, parodied in Algernon's "Bunburying," is the notion of the countryside as pastoral, traditional, and morally good and the city as associated with decadence and vice.
Much of the social anxiety readers see in Lady Bracknell and her daughter is the result of the rise of a wealthy industrial class. This meant that money was no longer the exclusive property of the landed aristocracy, and thus the insistence in the play on such things as addresses, manners, and relatives is a way of distinguishing class despite the spread of wealth. The inversion of hierarchy, where Lane becomes an arbiter and model of morality, also addresses the same social anxiety.
Perhaps the greatest social change seen in the play is the decline of the practical role of the aristocracy and its descent into frivolity and quest for status. The traditional "country squire" had been a farmer. He would be responsible for managing large amounts of land and an agricultural workforce. He would often serve as a magistrate, act as a patron to the parish church, offer reading lessons, and generally be a crucial part of village life. In Wilde's play, readers see an aristocracy living off rents or invested funds, unmoored from local country duties, living essentially trivial lives, pursuing pleasure and prestige but not really having a greater purpose in life.