In "Araby," how does Mangan's sister illustrate some of Joyce's judgments about the relationship of the Irish people to the church?
Like the narrator, Mangan's sister lives on North Richmond, literally and figuratively a quiet, dead-end street. The neighborhood consists of Irish families living "decent lives," within houses that "gazed at one another with brown imperturbable faces." North Richmond is described in the story in terms of darkness and poverty:
. . . our play [the narrator and the other children's outdoor activities] brought us through the dark muddy lanes behind the houses . . . to the back doors of the dark dripping gardens where odors arose from the ashpits, to the dark odorous stables . . . .
In this setting at night, "the lamps of the street lifted their feeble lanterns."
In Joyce's story, the Irish of North Richmond Street attempt to escape the hopelessness of their lives in various ways, often by turning to the church. Mangan's sister seems to be one of them.
As described by the narrator, she is a beautiful, desirable young woman:
The light from the lamp opposite our door caught the white curve of her neck, lit up her hair that rested there and, falling, lit up the hand upon the railing. It fell over one side of her dress and caught the white border of a petticoat . . . .
Amid the darkness, Mangan's sister stands in a pool of light, her beauty emphasized. She wears a silver bracelet, and as she speaks to the narrator, she turns it "round and round her wrist." Mangan's sister would "love to go" to Araby, saying it would be a "splendid bazaar." She thinks the narrator is fortunate to be able to attend. She, however, cannot go because she will be attending a retreat in her convent, the school she attends under the supervision of Catholic nuns.
In her youth and beauty, adorned with a bit of silver in the midst of gray poverty, Mangan's sister is called away from life by the church; although she longs for the excitement and diversion of Araby, she will answer the call and attend the religious retreat. Turning her silver bracelet "round and round" as she speaks suggests restlessness, implying an inner conflict between what Mangan's sister really wants and what the church expects of her. Thematically, her individuality and personal desires (and perhaps her needs) are subjugated by the church.
In "Araby," the narrator as a young boy is infatuated with Mangan's sister. He has been educated by the church and is a young adolescent, so he combines the religious and the secular and sees the girl he has a crush on as a pure, religious woman. She becomes almost a virgin Mary figure to him. He imagines himself as a religious, saintly warrior coming to her rescue.
He comes to see the silliness of his view of his relationship with Mangan's sister, if you can call it a relationship. It, to the boy, becomes as trivial as the conversation he overhears at the bazaar. He is disillusioned, you could say, or awakened and granted sight into the truth. His blind illusions are stripped from him.
I'm not sure I would recommend looking for a symbol here, but if you must, you could draw parallels between the boy's "worship" of the girl and Irish illusions about the church. Joyce believed that the Irish Catholic Church stifled the development of its members. His problem in the story and some of his other fiction isn't with belief in God, but in what organized religion has done to belief in God.
You might be able to argue, then, that the relationship between the boy and the girl represents blind allegiance and illusion. The Irish people, you could say, hold on to illusions and are blind when it comes to the church.