Did a 2 month job across the road from a similar car wash. Saw all kinds of strange things being washed there. We just had to shut down one day and go across the road.....a fellow was washing down two B-29 radial engines. One had a couple of cylinders off so we other see inside. Remarkable engines.
The water at a Car Wash is recycled consequently the trap in the floor catches all the "mud" off from your Truck after you have been out 4-wheeling all day. They don't want to deal with it being on the floor with the next Customer complaining plus the fact that it would have to be shoveled out of the trap/separator, consequently the sign stating "No Trucks!" If it was just some Min-Wage person for the Attendant, whats he care? If it was the Owner, he may have complained about you depositing "construction dirt" in his Wash Bay.
As far as washing Show Tractors, it gets done here all the time too! 👍