Answer
I say, and with God's help: It is noted that if all the characteristics of water change in color, taste, or smell due to mixing with soap without cooking, it remains pure and purifying for ritual impurity, thus it is permissible to remove actual impurity with it, and it is permissible to perform ablution and bathing with it. However, if all the characteristics of water change in color, taste, or smell due to mixing with soap after being cooked with water to the point that it becomes thick, it becomes pure but not purifying for ritual impurity, thus it is permissible to remove actual impurity with it, but it is not permissible to perform ablution and bathing with it; as narrated by Ibn Abbas: "A man fell from his camel and died, so the Prophet (peace be upon him) said: Wash him with water and sidr...", in Sahih Muslim 2: 865, and Sahih Bukhari 1: 425. And from Qais ibn Asim: "He came to the Prophet (peace be upon him) and he ordered him to bathe with water and sidr", in Sunan al-Bayhaqi al-Kabir 1: 172. And from Umm Hani, may Allah be pleased with her, she said: "The Messenger of Allah (peace be upon him) was on the day of the conquest at the top of Mecca, and I came to him, and Abu Dharr brought a bowl containing water, and I said: I see in it traces of dough, so Abu Dharr covered it and bathed, then the Prophet (peace be upon him) covered Abu Dharr and he bathed" in Sahih Ibn Khuzaymah 1: 119, and Sahih Ibn Hibban 3: 462, see: Umdat al-Ri'ayah 1: 85, and Allah knows best.