Place spaghetti squash cut-side-down on a microwave-safe plate. Stab a few small holes into the squash. Microwave on high until tender, about 10 minutes.
Heat a small pot over medium-low heat. Add cream cheese; cook and stir until melted, about 4 minutes. Add Buffalo sauce; stir until combined. Mix in chicken breast and ranch dressing. Remove from heat.
Scrape all the squash flesh into the center of each half using a fork. Pour Buffalo-chicken mixture on top; sprinkle with shredded Cheddar-Monterey Jack cheese and blue cheese.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Bake under the preheated broiler until cheese is bubbling and golden, about 5 minutes.