Soften the cream cheese: Leave the cream cheese on the counter for about 30 minutes until it gives easily when pressed. This prevents lumps once it's mixed with the hot sauce and dressing.
Preheat the oven: Set the oven to 375°F and lightly grease a 9-inch baking dish so the dip doesn't stick to the edges.
Mix the cream cheese base: In a large bowl, beat the softened cream cheese with the hot sauce and ranch or blue cheese dressing until smooth and pale orange, about 2 minutes.
Fold in the chicken: Add the shredded chicken to the bowl and stir gently until it's evenly coated but still visible in shreds, not fully blended into the base.
Spread into the dish: Press the mixture into the prepared baking dish in an even layer, smoothing the top with a spatula.
Top with cheese: Scatter the shredded cheddar and Monterey Jack evenly over the surface so the whole top is covered.
Bake until bubbling: Bake for 20 to 25 minutes, until the edges bubble and the cheese turns golden in spots.
Rest briefly: Let the dip sit for 5 minutes out of the oven so it firms up slightly and is easier to scoop.
Add toppings: Sprinkle the crumbled turkey bacon and sliced green onions over the top for color and crunch.
Serve warm: Set out celery sticks, carrot sticks, and chips alongside the dip while it's still warm from the oven.