Preheat oven to 350 degrees F (175 degrees C). Grease two 8x4-inch loaf pans.
Beat white sugar, brown sugar, butter, and applesauce together in a bowl using an electric mixer until light and fluffy. Beat egg and egg whites into sugar mixture; stir in bananas, vanilla extract, and cinnamon. Mix flour, alternating with buttermilk, into sugar mixture until batter is well mixed; fold in pineapple and cherries. Pour batter into the prepared pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 55 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
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