The conventional notions of sex and gender are greatly challenged in The Importance of Being Earnest. The prudish, demure, and submissive Victorian female specimen is nowhere to be seen in the play, not even in the figure of the sanctimonious Miss Prism.
Instead, what we find is a group of strong, opinionated, unconventional females who say what they feel, argue against the "propriety" of things and fight for what they want.
In Gwendolen we find a woman who goes against the wishes of her mother and even goes as far as driving into the country (alone!) to find Jack's country estate. Once there, she has her showdown with Cecily after thinking that she is engaged to HER Ernest and all of this prompts that Lady Bracknell chases after her to retrieve her.
Cecily, the other half of the showdown, has no fear in stating her intentions to marry "an" Ernest, and she shows a fearful sense of independent thinking with that diary onto which she records events of her life that have never happened. Nevertheless, she is far from the obedient servant woman; after all, she went for Algernon of all characters, precisely because she thought that he was the "bad" brother Ernest...isn't there a wild streak there somewhere?
Miss Prism, who is obviously flirtatious with Dr. Chausible seems to chastise everyone but when you look into her life you realize that she, too, has been rebellious enough. Where was she after she "accidentally" left baby Jack in the cloak room of Victoria Station? What did she do with her life to escape that?
Lady Bracknell, out of all the characters, may look like a proper Victorian except that when she talks about her husband she does it with very little concern and absolutely no admiration. A far cry indeed from the devoted wife.
As far as the males, Algernon represents the incorrigible dandy bachelor whose amoral behavior provides the flavor of the play, as he could care less about social expectations. Jack is the same way; after all, he does lead a double life pretending to be "Jack in the country and Ernest in the city". Hence, none of them are the chivalrous and impeccable males that would represent the Victorian ideal. In all, Wilde's purpose is to instill the sense of triviality among his characters; that is why the comedy is deemed as "trivial".