Bring a large pot of salted water to a boil. Cook the linguine until al dente, then reserve 1 cup pasta water and drain.
Pat the shrimp dry and season with salt, pepper, and paprika.
Heat the olive oil in a large skillet over medium-high heat. Cook the shrimp for 1 to 2 minutes per side until pink and just cooked through. Transfer them to a plate.
Reduce the heat to medium and melt the dairy free butter. Add the garlic and cook for 30 seconds.
Pour in the white wine and simmer for 2 minutes, then add the coconut milk, nutritional yeast, lemon juice, and red pepper. Simmer for 3 to 4 minutes.
Add the linguine and 1/4 cup pasta water to the skillet. Toss until the sauce coats the pasta, adding more pasta water as needed.
Return the shrimp to the skillet, toss gently, and garnish with parsley before serving.