What do the references to mythology and religion have to do with the poem "Sunday Morning"?
The poem contains a dialogue or a conversation between the woman, who is on a journey to try and understand the value of her earthly life as opposed to her spiritual life, and the poet who is helping her decide.
Religion is a part of this poem because the woman is relaxing on a Sunday morning, lingering over coffee and fruit, instead of going to church. She considers the Christian tradition that requires mass attendance on Sunday and there is a suggestion that it is actually Easter Sunday, the holiest day on the Christian calendar.
Initially she feels content with her decision to enjoy the beauty of this Sunday by relaxing in the Sun, but then she realizes that her existence is only temporary, and unlike spiritual things which are eternal, her life will fade.
She then expands her thinking to include Greek mythology, mentioning Jove and how disconnected he was from an earthly life, he had no connections to nature like she does.
In the end, the poet and the woman decide to abandon the traditional Christian form of worship because she feels that it does not hold any promise except the coldness of the grave.
She embraces a life of earthly pleasures, a pagan lifestyle that makes her feel free to seize the day.
In "Sunday Morning" by Wallace Stevens, the allusion to mythology and religion are part of the speaker's argument that nature and religion are not in conflict with one another, but, rather connected.
In stanza three, the speaker connects the "inhuman birth" of Jove to the birth of Christ by connecting arguing that Joeve "moved among us" until "our blood," meaning the human birth of Jesus Christ "commingl[ed]" with the heavens, bringing "such requital to desire" that the star over Bethlehem became the sign of this communion of the natural world with the spiritual world (religion):
Shall our blood fail? Or shall it come to be
The blood of paradise? and shall the earth
Seem all of paradise that we shall know?
This third stanza is the pivotal stanza of the poem as the speaker makes his strongest point in his argument to the woman that the natural world is more eternal than that of the spiritual, and that in appreciating the natural world, she also appreciates the spiritual.