The speaker has been shut inside all day, and what comes over them is a strange, specific craving. They don't want a meal exactly. They want to eat a stomach, one that is "green and full / as an old religion." The wish is odd, even a little unsettling, and that's much of its charm.
The title helps. "Rumination" suggests chewing things over in the mind, but it also points to animals that chew cud and have stomachs built for digesting grass. Read that way, the green stomach is a grazer's stomach, packed with plants, and the speaker's hunger is really a longing for the outdoors: for green, growth and the natural world they've missed. That is an inference, but the imagery supports it.
The comparison to "an old religion" adds weight. It makes the fullness feel ancient, deep and almost sacred. The mood is earthy and slightly wry, a restless, bodily yearning to get out of the house and take in something living.