Preheat the oven to 450°F. (If you have a pizza stone, place it on the middle rack in the oven before preheating.)
Ensure that the pizza dough has risen properly, then stretch it into a 12- to 14-inch circle on a large sheet tray (or piece of foil sprayed with olive oil spray if you are baking with a pizza stone).
In a medium bowl, stir to combine the buffalo sauce and ranch dressing. Spread one-half of this mixture all over the pizza crust, leaving about a 1-inch border at the edges. In the same bowl, toss the shredded chicken with the remaining sauce mixture.
Sprinkle the mozzarella and blue cheese in an even layer over the top of the pizza sauce. Top evenly with the chicken and red onion.
Bake for 10 to 12 minutes, until the edges are golden and the cheese is melted all over. (If you use a stone, place the entire piece of foil with the pizza on the stone. If you make the pizza on the sheet tray, you can either place that on the stone or the oven rack.)
Drizzle with more buffalo sauce and/or ranch dressing if you like and top with green onions and parsley.
Notes
The best store-bought pizza dough to use: You can use a ball of fresh pizza dough purchased from the refrigerated section of the grocery store. The dough should weigh about 12 to 16 ounces in order to be the correct size for this recipe. I do not recommend using canned pizza dough.
If your dough feels sticky or tacky, lightly flour the dough and baking sheet before shaping the dough. For the pan, you can use all-purpose flour, semolina, or fine cornmeal. Use regular AP flour for the dough, if needed.
If you want to use a pizza stone, place it on the middle rack in the oven before preheating the oven. Stretch the pizza dough on a piece of aluminum foil sprayed with olive oil to prevent sticking. When ready to bake, place the piece of foil with the assembled pizza on it directly onto the pizza stone.