Preheat your oven to 350°F (175°C) and line a 9×5-inch loaf pan with parchment paper, leaving some overhang for easy removal. Lightly grease any exposed parts of the pan.
Prepare your fruit carefully. Dice the rhubarb into approximately 1/4-inch pieces, removing any leaves (they’re toxic) and stringy outer parts. Hull and dice the strawberries into similar-sized pieces. Toss both fruits with 2 tablespoons of flour in a small bowl until coated. This prevents them from sinking to the bottom of your bread.
Whisk together the dry ingredients in a medium bowl: flour, baking soda, salt, and cinnamon until well combined.
In a large bowl, mix the wet ingredients. Whisk together the granulated sugar, brown sugar, and oil until combined. Add eggs one at a time, beating well after each addition. Stir in vanilla extract and buttermilk until the mixture is smooth.
Combine wet and dry ingredients gently. Add the flour mixture to the wet ingredients and stir just until no dry streaks remain. Overmixing will result in a tough bread, so use a light hand!
Fold in the prepared fruit mixture with a rubber spatula, taking care not to crush the berries too much. A few gentle strokes should distribute them evenly.
Transfer batter to the prepared loaf pan and spread evenly. If using, sprinkle turbinado sugar over the top for a delightful crunch.
Bake for 55-60 minutes until a toothpick inserted in the center comes out clean or with a few moist crumbs. If the top begins to brown too quickly, loosely cover with aluminum foil after about 40 minutes.
Cool in the pan for 15 minutes, then use the parchment paper overhang to lift the bread out. Let it cool completely on a wire rack before slicing to prevent it from falling apart.