As your question implies, a primary characteristic of Emily Dickinson's poetry is a blend of at least two literary traditions--romanticism or naturalism, on one hand, and realism, on the other. Dickinson's poetry find its settings not in the structures and belief systems of formal religion but in settings created by nature and nature's God. Her tendency to look within herself for her religion is also a product of her readings of the transcendentalists like Emerson and Thoreau.
For example, in her poem "Some keep the Sabbath going to Church--," Dickinson places herself squarely in the romantic/naturalistic tradition when she writes
Some keep the Sabbath going to Church--/I keep it, staying at Home--/With a Bobolink for a Chorister--/And an Orchard, for a Dome--
As in many of her poems, here Dickinson argues that she does not need formal religion in order to "keep the Sabbath," a phrase normally associated with a person's going to a formal church service. Instead of finding religion within the confines of a conventional church, Dickinson finds religion in her home, specifically, in her own backyard. The sexton, a person who usually assists a minister during church service, has become, in Dickinson's personal "church," a singing bird, and the dome of the church is an orchard rather than a steeple. Dickinson worships--as many romantics did--nature and nature's creations.
Dickinson's poems could also be relentlessly realistic. When she writes that
I like a look of Agony,/Because I know its true--/Men do not sham Convulsion,/Nor simulate a Throe--
she has entered poetic territory that is unique for her time and place. The very fact of the poem is testament to Dickinson's interest in realism--no female poet of her time wrote so starkly about the human condition and on such a personal level. The subject itself--a preference for the real over the "politically correct"--startled her readers as her poems began to be circulated after her death simply because such themes were not the usual or accepted subjects of poetry. Her ability to articulate reality, as she does in this poem, made her poetry seem at odds with her time, and we still consider many of her poems to be "modern" in their attachment to realism.