Preheat an oven to 350 degrees F (175 degrees C). Combine the flour, baking soda, baking powder, and salt in a bowl.
Beat the shortening, white sugar, and brown sugar with an electric mixer in a large bowl until smooth. Beat in one egg until completely incorporated. Beat in the last egg. Mix in the flour mixture until just incorporated. Fold in the white chocolate chips, blueberries, and cranberries; mixing just enough to evenly combine. Roll the dough into walnut-sized balls and place 2 inches apart onto ungreased baking sheets. Flatten each ball to about 1/2-inch thick.
Bake in the preheated oven until golden brown, 10 to 12 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
