Combine chicken, broth, diced tomatoes, white beans, chilies, wing sauce, corn, celery, onion powder, garlic powder, white pepper, and salt in a 6-quart or larger slow cooker.
Cover crock pot and cook on LOW for 5 hours.
Add cream cheese and cover and cook on LOW 30 more minutes. Open slow cooker and remove chicken. Add Monterey Jack cheese and sitr until cream cheese and Monterey Jack cheese are melted and blended in.
Shred chicken and return to slow cooker. Dish into bowls and top with blue cheese crumbles and green onions.