Preheat oven to 350 degrees F (175 degrees C). Line 12 muffin cups with paper muffin liners.
Stir rhubarb, all-purpose flour, whole wheat flour, 1/2 cup brown sugar, baking soda, salt, and 1/2 teaspoon cinnamon together in a large bowl.
Whisk yogurt, oil, and egg together in a separate bowl; pour into rhubarb mixture and stir until just combined and batter has a thick, dough-like consistency. Spoon batter into muffin cups.
Stir 1/4 cup brown sugar, rolled oats, melted butter, and 1/2 teaspoon cinnamon together in a small bowl; top batter with about 1 tablespoon of oats mixture.
Bake in the preheated oven until golden, about 20 minutes. Cool 15 minutes before removing to wire rack.
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