Hi, washing up liquid contains A LOT OF SALT, don't use it. It sneaks through seams, behind trim and chances are you won't get rid of it all.
That is obvious correct, but the roads are covered with salt all through the winter months which will get into every nook and cranny like seams and trim as well as underneath, all over the exposed suspension and such and this will be in contact with the body/paintwork for far longer than a wash with fairy liquid.
Although I wouldn’t use it myself, some of the detailing guys use it for the very purpose of stripping wax etc and I doubt as a one off any harm would result.