Yes. Nonabrasive dish soaps are safe to use when washing a car. Soap maker Dawn even recommends using its dishwashing soap to remove grease and grime from exterior car surfaces. Although dishwashing soap is acceptable under certain circumstances, it should never be the first choice for a well-maintained car. Dish soap is so effective at its job that it will remove more than just stubborn contamination. It will remove any previously applied car wax or paint sealant and leave the paint unprotected.
Despite what some say, some dish soaps are nonabrasive. Some manufacturers, like Palmolive, say on their websites that their soaps contain no harsh abrasives. Suppose you find yourself in a pinch needing to remove stubborn grime from a car’s paint and don’t have car shampoo available or want to strip off any previously applied paint protection products before adding a new layer. In those cases, dish soap is a perfectly safe soap substitute.