The Importance of Being Earnest does not really contain any religious themes. However, in Act II, the practice of christening does become an important issue. Both Jack and his friend Algernon are engaged to young women who think that only a man named Ernest is worth marrying. They are both in agreement on that point. Of course, neither Jack or Algernon is named Ernest; the name is one that Jack made up for his imaginary brother, whom he becomes when he goes to London. Algernon has stolen the name and is pretending to be Jack's brother Ernest. Since neither woman will marry anyone but an Ernest, they both wish to be christened, or baptized, in the Anglican faith, and have their names changed to Ernest to please their fiancees.
Act II does contain a brief mention of some of the duties of Canon Chasuble, the Anglican priest who lives in the area of Jack's country property; one of those duties is christening, both adults and babies, but, thematically, the play does not really touch on anything of a religious nature.
There is an element of satire of relgious mininsters such as Dr. Chausible who claims to have one perfect sermon that he would be happy to proclaim at the upcoming baptisms. The satire comes from the fact that he has given this exact sermon at any number of previous events and no matter what the occasion, it seems to suit the situation -- baptism, wedding, funeral. Wilde seems to be suggesting that the clergy didn't have much original material or creative and inspiring teaching for the weekly sermons and therefore tended to "recycle" the same old lessons for all services. The title Doctor suggests a well educated man, and he shows an ability to draw metaphors from various fields, such as horticulture, but in actually, he is tired and uninspired.