Preheat your grill to medium-high heat.
In a large bowl, combine the Cajun seasoning, olive oil, garlic powder, onion powder, smoked paprika, salt, and pepper. Add the chicken thighs and toss to coat evenly. Let marinate for at least 30 minutes.
While the chicken is marinating, prepare the Alabama white sauce. In a medium bowl, whisk together the mayonnaise, apple cider vinegar, Dijon mustard, lemon juice, Worcestershire sauce, garlic powder, black pepper, and cayenne pepper until smooth. Refrigerate until ready to use.
Once the grill is hot, place the marinated chicken thighs on the grill. Cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F.
Remove the chicken from the grill and let it rest for 5 minutes before slicing.
Serve the grilled chicken with a generous drizzle of Alabama white sauce on top or on the side for dipping.