Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x5-inch loaf pan.

Stir together flour, sugar, baking powder, baking soda, and cinnamon in a large bowl. Beat together egg, applesauce, and butter in a separate bowl. Stir applesauce mixture into flour mixture just until combined. Fold in walnuts and raisins; pour batter into prepared loaf pan.

Bake in the preheated oven until a toothpick inserted into the center of the loaf comes out clean, about 45 minutes. Allow to cool before slicing.