Assalamualaikum ustaz. Is it permissible for us to use domesticated donkey milk soap, especially if it is for the treatment of some skin condition? Thank you.
Waalaikumussalam wrt. wbt.,
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions, and all those who follow his footsteps until the Final day.
We start with the statement of Allah SWT:
وَاقْصِدْ فِي مَشْيِكَ وَاغْضُضْ مِن صَوْتِكَ ۚ إِنَّ أَنكَرَ الْأَصْوَاتِ لَصَوْتُ الْحَمِيرِ
“And be moderate in your pace and lower your voice; indeed, the most disagreeable of sounds is the voice of donkeys.” 
This verse contains advice for us to not walk with arrogance. ‘Ata’ stated that it means to walk calmly and don’t rush. Then, we are also reminded to lower our voices and not talk loudly unnecessarily, for talking loudly without any need will disturb others who are listening.  The reason is the most disagreeable voice is the voice of a donkey for its characteristic stupidity and loud sound. 
Domesticated donkeys are prohibited to be eaten
The majority of scholars are of the opinion that the meat of domesticated donkeys is prohibited to be eaten.  Furthermore, Ibn Qudamah cited Ibn ‘Abd al-Bar saying that there isn’t any khilaf among the Muslim scholars to this day of the prohibition of the meat of domesticated donkeys. Moreover, some companions narrated from the Prophet PBUH regarding the prohibition of this meat such as Ali bin Abu Talib, Abdullah bin Umar, Abdullah bin ‘Amr, Jabir, al-Bara’, Abdullah bin Abu Aufa, Anas and Zahir al-Aslami with sahih and good sanad. 
This prohibition is based on the narration from Ali bin Abu Talib RA, he said:
أَنَّ رَسُولَ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ نَهَى عَنْ مُتْعَةِ النِّسَاءِ يَوْمَ خَيْبَرَ، وَعَنْ أَكْلِ لُحُومِ الحُمُرِ الإِنْسِيَّةِ
“At the battle for Khaibar God’s Messenger forbade the temporary marriage (mut’a) of women, and eating the flesh of domestic asses.” 
Furthermore, Ibn Qudamah also said that its prohibition is clear because it eats filth according to the narration of Abdullah bin Abu Aufa.  Whereas Anas bin Malik RA narrated on the day of Khaibar, Rasullullah PBUH asked for an announcement to be made:
إنَّ اللَّهَ وَرَسُولَهُ يَنْهَيَانِكُمْ عَنْ لُحُومِ الْحُمُرِ فَإِنَّهَا رِجْسٌ أَوْ نَجِسٌ
“Allah and His Messenger have prohibited for you (eating of) the flesh of the donkeys, for it is unclean.” 
Hence, it is clear that among the reasons for the prohibition of domesticated donkeys is because of its najis characteristic.
Using domesticated donkey milk soap
We should first know that the milk of domesticated donkeys is najis. The reason is the milk of an animal that is impermissible to be eaten such as domesticated donkey and others is najis because the ruling of milk is the same as the meat and its meat is considered najis. Hence, it is prohibited to be drunk except for the milk of a human even if the meat of a human is prohibited to be eaten her milk is pure and clean. 
Coming back to the question asked, scholars have discussed this matter in their books regarding the ruling of using soap made from najis ingredients. According to the chosen opinion of scholars in madhhab Hanafi, soap made from oil that came into contact with najis or mutanajjis is pure. Hence, it is permissible to use and trade it. 
Likewise, scholars of madhhab Syafi’I also agreed with the opinion that states using soap made from najis oil is permissible. Regarding this matter, Syeikh al-Islam Zakaria al-Ansari cited from al-Majmu’ that it is permissible to smear the fat of animal carcasses, manufacture soap from oil that has najis, feed animal carcasses to dogs and birds as well as feed food that has came into contact with najis (mutanajjis) to farm animals. 
Moreover, al-Ramli explained saying a person is permissible to use soap made from oil that has najis on his body and clothes. Then, he washes it – the soap from his body and clothes. 
Medical treatment using najis material
Regarding this matter, there is a hadith narrated by Ummu Salamah R.Anha, where Rasullullah PBUH said:
إنَّ اللَّهَ لَـمْ يَجْعَلْ شِفَاءَكُمْ فِيمَا حرَّمَ عَلَيْكُمْ
“Allah did not make your cure in what He made Haram (unlawful) to you.” 
Furthermore, there is also another hadith as narrated by Wa’il al-Hadrami, that Tariq bin Suwaid al-Ju’fi RA asked Rasullullah PBUH regarding wine. Then, the Prophet PBUH forbade – or disliked for him to do it. – Tariq said: “When I told him that he made it only as a medicine he replied,”
إِنَّهُ لَيْسَ بِدَوَاءٍ، وَلَكِنَّهُ دَاءٌ
“It is not a medicine, but is a disease.” 
Imam al-Nawawi when he commented on the issue of treatment using najis, explained according to the opinion of madhhab Syafi’I and the majority of scholars that treatment with najis is permissible except for something intoxicating. However, the permissibility is bound to the unavailability of pure and halal medicine or treatment to be used. If there is any pure or halal treatment, then using material that has najis such as medicine is prohibited without any khilaf. 
According to the above discussion and arguments, in our opinion, it is permissible to use domesticated goat milk soap on one’s body and clothes. Thus, using it for medicinal purposes is surely permissible. However, afterwards, it must be washed from one’s body and clothes from any trace of the soap with clean water to purify it.
However, we would like to suggest that if there isn’t any necessity to use the soap, then it is best to avoid using it, for it is closer to the character of a Muslim that loves cleanliness and avoid any filth or najis. Especially, when soap is included in tahsiniyyat (additional value) and not hajiyat (necessity) or darurat (exigent need).
May Allah SWT grant us all a clear understanding in religion. Amin.
 Surah Luqman: 19
 See Zubdah al-Tafasir min Fath al-Qadir, pg. 541.
 See al-Tafsir al-Muyassar, pg. 412.
 See al-Majmu‘ Syarh al-Muhazzab, 9/6.
 See al-Mughni, 9/407.
 Narrated by al-Bukhari (4216) and Muslim (1407)
 See al-Mughni, 9/407.
 Narrated by al-Bukhari (4198) and Muslim (1940)]
 See al-Fiqh al-Manhaji, Pub. Dar al-Qalam, 1/40; 1/503 and al-Taqrirat al-Sadidah, pg. 128.
 See al-Mausu‘ah al-Fiqhiyyah al-Kuwaitiyyah, 26/301.
 See Asna al-Matalib, 1/278.
 See Nihayah al-Muhtaj, 2/384-385; Hasyiah al-Ramli ‘ala Asna al-Matalib, 1/278.
 Narrated by Ibn Hibban (1391)
 Narrated by Muslim (1984)
 See al-Majmu‘ Syarh al-Muhazzab, 9/50-51