I simply tell them that we do not install customer supplied parts. If they ask why I tell them that labor alone is not enough to cover all of our overhead expenses: i.e. rent, taxes, equipment, etc. and that we make money on parts. This is necessary for us to provide warranties and stay in business, I suggest they look for a small shop that doesn't stay as busy as we stay. If they want to supply something like a water pump or heater core I explain that that is not smart at all from a warranty standpoint due to the fact that labor is the big cost in these situations.
Invariably with customer supplied parts you run into situations that it is the wrong diagnosis, the wrong part, or you are having to straighten out other things done improperly. If we drive enough of the right kind of business to the shop we can let other shops deal with these time wasting less propfitable jobs.
I do make exceptions sometimes. Occassionally I will take something if we are really slow or if someone has some custom performance parts.