Does soap become impure when used to wash the private parts, and is it permissible to use it afterwards for other purposes?

If solid soap is afflicted with impurity, the impurity itself must be removed for it to be considered pure and permissible to use. However, if the soap is liquid and is afflicted with impurity that changes its color, taste, or smell, then it becomes impure and impermissible to use, and it must be poured away, because the substance of the impurity remains in it. If the impurity does not change any of the characteristics of the liquid soap, then it remains pure and permissible to use.