Bring a large pot of salted water to a boil and cook pasta until al dente. Drain, rinse under cold water, and let cool completely.
Shred rotisserie chicken into bite-sized pieces. Chop celery, bell peppers, and onion into small, even pieces.
In a large bowl, combine mayonnaise, yogurt, Dijon mustard, lemon juice, garlic powder, salt, and pepper. Stir until smooth and adjust seasoning if needed.
Add cooled pasta, shredded chicken, chopped vegetables, and cheese to the bowl with dressing. Toss gently until evenly coated, then fold in parsley if using.
Cover and refrigerate for at least 30 minutes before serving. If too thick after chilling, add a spoonful of yogurt or splash of lemon juice.