Preheat oven to 350 degrees F (175 degrees C). Grease an 8×4-inch loaf pan.
Spread walnuts onto a baking sheet.
Bake in the preheated oven until toasted and fragrant, 5 to 10 minutes. Set aside to cool.
Mix dates, figs, butter, and baking soda together in a bowl. Pour boiling water over the date mixture. Let sit for figs to slightly rehydrate, 15 to 20 minutes.
Stir sugar, walnuts, and eggs into date mixture. Whisk all-purpose flour, whole wheat flour, salt, and baking soda together in a separate bowl. Stir flour mixture into date mixture until batter is just combined. Pour batter into the prepared loaf pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 55 to 65 minutes. Cool in the pan for 10 minutes before removing to cool completely on a wire rack.