Soften the cream cheese: Let the cream cheese sit at room temperature for about 1 hour until it gives easily when pressed with a spoon. Cold cream cheese will leave lumps in the finished dip.
Preheat the oven: Set the oven to 375°F and lightly grease a 9-inch baking dish. Make sure the rack is set in the center of the oven.
Beat the cream cheese base: In a large bowl, beat the softened cream cheese, buffalo sauce, ranch dressing and garlic powder with a hand mixer until smooth and pale orange, about 2 minutes.
Fold in the chicken: Add the shredded chicken and stir gently with a spatula until just combined, keeping the chicken in loose shreds rather than mashing it into the base.
Spread into the dish: Transfer the mixture to the prepared baking dish and press it into an even layer with the back of a spoon, reaching into the corners.
Add half the cheddar: Sprinkle 3/4 cup of the shredded cheddar evenly over the chicken mixture so it melts into the dip while baking.
Top with remaining cheese: Scatter the rest of the cheddar over the top along with the blue cheese crumbles, covering the surface edge to edge.
Bake until bubbling: Bake for 20 to 25 minutes, until the edges bubble and the cheese on top turns light golden in spots.
Rest before serving: Let the dip rest for 5 minutes out of the oven so it firms up slightly and is easier to scoop.
Garnish and serve: Scatter the sliced green onions over the top and serve warm with celery sticks and tortilla chips.