Preheat the oven to 200°C (400°F)
Add the white rice flour, tapioca flour, corn starch, brown rice flour, xanthan gum, baking powder, salt, brown sugar, and white sugar in a bowl. Whisk the ingredients and combine them. Then add the cranberries and mix them with the dry ingredients using a spatula. This will help to keep the cranberries whole.
Add the vegetable oil, eggs, lemon zest, lemon juice, buttermilk, and vanilla extract in a separate bowl. Whisk the ingredients together. Then add the dry ingredients and gently mix them using a spatula. The batter will be thick.
Align a muffin tin or a cupcake tin with muffin liners. Fill the liners all the way to the top with cranberry orange muffin batter.
Bake the muffins at 200°C (400°F) for the first 5 minutes, then reduce the heat to 180 °C (356°F) and bake them for another 10-15 minutes or until a toothpick inserted at the center comes out clean. Allow the muffins to cool in the tin for 5 minutes before transferring them to a cooling rack.