Does doubt regarding the impurity of clothes, or the persistence of a trace of the color of impurity after washing them, necessitate washing them again and render what they touch impure?

It appears that you are afflicted with some form of waswasa (whispers/obsessive thoughts). You must ignore it and pay no attention to it. The basic principle concerning things is purity, so do not pay attention to doubts. This is part of the ease of Sharia. If you are certain that there is impurity on your clothes, wash the impurity outside the washing machine first. You are not required to wash the entire garment, but only the impure spot.