Melt butter in a large skillet over medium heat, and cook and stir the onion, green pepper, celery, salt, cayenne pepper, and white pepper until the vegetables are tender and the onion is translucent, about 5 minutes. Stir in the tomatoes and crawfish tails, reduce heat to medium-low, and cook for about 3 minutes to blend flavors, stirring occasionally.
Whisk flour and water together in a bowl until the mixture is smooth, and pour the flour mixture into the skillet. Bring the filling to a simmer, and cook, stirring constantly, until the mixture thickens, about 5 minutes. Remove from heat and allow to stand for 20 to 30 minutes to finish thickening.
While filling is cooling, preheat oven to 400 degrees F (200 degrees C). Pour the filling into the prepared pie crust, and bake in the preheated oven until the crust is golden brown and the filling is hot and bubbling, 30 to 40 minutes. Cool for 10 minutes before serving.
