Preheat the oven to 375°F (190°C). Line two 12-count muffin pans with 15 muffin liners and set aside.
In a large mixing bowl, whisk together the all-purpose flour, whole wheat flour, baking soda, baking powder, cinnamon, and salt until well combined. Set aside.
In a separate large mixing bowl, whisk together the oil, brown sugar, applesauce, eggs, and vanilla extract until fully combined. Add the grated carrots, shredded apples, shredded coconut, raisins, and walnuts to the wet ingredients and stir until well combined.
Add the dry ingredients to the wet ingredients and mix the two together until just combined.
Scoop the batter into the muffin liners, filling each one all the way to the top.
Bake for 20 to 25 minutes or until the tops of the muffins are set and a toothpick inserted into the center comes out clean. Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.