An economic environment of extreme poverty would affect both soap and cars, but not to the same degree. Soap is a necessity, whereas cars are not. So people would still have to buy soap, but they might switch to cheaper brands in a bad economy so I would still worry if I were manufacturing soap.
No, they won't be similarly affected. Soap powder is much more of a necessity. It is also something that costs relatively little when compared to a motor vehicle. If there is a recession and people have less money, they will still need to buy soap powder and will still largely be able to afford it. By contrast, people will be much more wary of buying a "big ticket" item like a car.