The one time I took my car to be washed by a business, they were extremely interested. One of the guys called a couple fellow workers over to come take a look at my new car
They had no problem once I explained how it worked, but I certainly trusted them since they seemed so concerned with it.
Why, exactly, do you not want them cleaning the LCD? I can tell you for a fact that any car washer has cleaned thousands of them. They've been in luxury cars for years.