Heat 1 tablespoon of coconut oil in a large skillet over medium-high heat.
Toss the shrimp with ½ teaspoon of salt, then add them to the skillet in a single layer. Cook for 1-2 minutes per side, until the shrimp are just cooked through. Transfer to a plate and cover to keep warm.
Heat the remaining tablespoon of coconut oil in the skillet over medium-high heat. Add the onion and parsnips and cook until tender, about 3-4 minutes.
Add the mushrooms to the skillet and cook until tender, about 3-4 minutes. Stir in the garlic and cook until fragrant, about 30 seconds.
Add the cabbage along with ½ teaspoon of salt. Cook, tossing occasionally, until the cabbage is wilted, about 3-4 minutes.
Pour in the coconut aminos and rice vinegar, and sprinkle in the Chinese five spice powder. Add the shrimp back to the skillet, toss, and cook for another 2-3 minutes, until heated through.
Stir in the lime juice and garnish with green onions before serving.