In a medium microwave-safe bowl, microwave the pistachios on high for 1 minute to toast them. Allow to cool completely, about 10 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, beat together the cream cheese, Cheddar cheese, mayonnaise, and milk until smooth. Add the parsley, vinegar, garlic salt, onion powder, white pepper, salt, and dill. Fold in the pistachios.
Transfer to a serving bowl, cover with plastic wrap, and refrigerate for 30 minutes to 1 hour before serving with crackers or pita chips.