Most modern detergents are low sudsing.
In the past I've seen someone put clothes washing powder in a black and gray tank. Ever seen a dishwasher after someone put laundry soap in it.
Occasionally I still see an RV sailing down the highway with a nice trail of soap bubbles coming out of the tank vents.
No harm, as long as the guy behind you with the soap covered windshield doesn't catch up with you at the end of the day.