You might like to consider the way in which Wilde satirises both of these institutions through their representative figures. Miss Prism for example is clearly his chief vehicle for satirising education. She, as a governess, is shown to be a neverending fountain of various cliches. Consider her first speech as she is introduced in Act II:
Surely such a utilitarian occupation as the watering of flowers is rather Moulton's duty than yours? Especially at a moment when intellectual pleasures await you. Your German grammar is one the table. Pray open it at page fifteen. We will repeat yesterday's lesson.
Such phrases, and Cecily's less than enthusiastic responses, clearly indicate the way in which Wilde is poking fun of education and its role in making us into respectable individuals.
Dr. Chasuble is likewise shown to be the representative of religion, but he is made into a figure of fun whilst trying to preserve his serious demeanour and harbouring a serious infatuation for Miss Prism at the same time. Notice what he says in the same act and how it makes him ridiculous:
Were I fortunate enough to be Miss Prism's pupil, I would hang upon her lips. I spoke metaphorically. My metaphor was drawn from bees. Ahem!
Trying to present himself as a serious and spiritual individual whilst making such hilarious faux-pas clearly indicates the way in which Wilde is satirising religion and showing its hypocrisy.