Assalamualaikum ustaz. Is it permissible to touch private parts with the right hand when washing up after urinating? Hope for an explanation.
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 begin with the statement of Allah SWT:
لَقَدْ كَانَ لَكُمْ فِي رَسُولِ اللَّهِ أُسْوَةٌ حَسَنَةٌ لِمَنْ كَانَ يَرْجُو اللَّهَ وَالْيَوْمَ الْآخِرَ وَذَكَرَ اللَّهَ كَثِيرًا
“There has certainly been for you in the Messenger of Allah an excellent pattern for anyone whose hope is in Allah and the Last Day and [who] remembers Allah often.” 
Commentary scholars explained that the above verse means that every word, action and situation of Prophet PBUH is a good example to follow so that all of us will follow it. Thus, hold unto the sunnah of the Prophet PBUH, for indeed it is held unto and followed by those who are hopeful (of blessings from) Allah and (rewards) the hereafter. 
Touching private parts with the right hand
Our teacher Syeikh Mustafa al-Khin stated that one should perform istinja’ (purification process after urination or defecation) using the left hand to wash the place where najis is excreted whether with water, stone or others, for this is the prioritized way. While istinja’ using the right hand is makruh the same as it is makruh to touch the penis with it. If one has to touch the penis to clean or wash it using stones or other solids, then one should hold the stone with the right hand without moving it, while the left hand holds the penis and moves this hand to clean the place where najis was excreted. 
In this matter, there is a hadith from Abu Qatadah, where the Prophet PBUH said:
إِذَا بَالَ أَحَدُكُمْ فَلاَ يَأْخُذَنَّ ذَكَرَهُ بِيَمِينِهِ وَلاَ يَسْتَنْجِي بِيَمِينِهِ وَلاَ يَتَنَفَّسْ فِي الإِنَاءِ
“Whenever anyone of you urinates, he should not hold his penis or clean his private parts with his right hand. (And while drinking) one should not breathe in the drinking utensil.” 
Regarding this matter, al-Bukhari named the chapter in his book as:
بَاب لَا يُمْسِكُ ذَكَرَهُ بِيَمِينِهِ إِذَا بَالَ
“Chapter of touching private parts with the right hand when urinating.” 
It can be understood from al-Bukhari’s naming that he signals the absolute restriction against touching private parts with the right hand only when urinating. Thus, other than when a person is urinating, it is permissible for him to touch his private part with his right hand. 
Abdullah al-Bassam stated that scholars differed on the ruling in the hadith bring about the meaning of whether it is makruh or prohibited. Scholars of madhhab Zahiri believes that the restriction is a prohibition according to the literal meaning of the hadith. While the jumhur of the scholars are of the opinion that it is makruh for the restriction is in the form of guidance and education and this is the strong opinion.
It is best if we bind any singular issue with a general syarak maxim. Among the maxims states that shariah came to celebrate maslahat (benefit) and rejects harm. Regardless of whether the maslahah is comprehensive or dominant. Likewise, shariah also came to restrict or prevent any mafsadah (harm), regardless of whether the restricted mafsadah is comprehensive or dominant. When we correctly applied or implemented the general maxim, then the ruling will become clear and apparent. Hence, as stated by jumhur of the scholars, it is included under the matters that are in the form of guidance, education and advice as well as included as matters of leaving makruh tanzih. 
Moreover, Abdullah bin Soleh al-Fauzan stated that this hadith shows the restriction against a person urinating while holding to his penis with his right hand because such an act contradicts the honour of the right. Jumhur of scholars understood this restriction as makruh as stated by al-Nawawi and others for it is included in matters of manners, guidance and advice. The same for it is included as matters in honouring the right. Thus, the restriction in this hadith doesn’t reach it to be prohibited.
This is different from Daud al-Zahiri and Ibn Hazm, for both of them ruled it prohibited, according to the original ruling of anything that is restricted is prohibited. However, in this issue, the opinion of the jumhur is stronger because the restriction is a form of education and guidance. This is strengthened with the statement of the Prophet PBUH regarding the penis, where the prophet PBUH said: “It is nothing but a part of your body.” 
Furthermore, al-Khattabi also said that the act of holding or touching the penis is ruled as makruh with the purpose of purifying it from having direct contact with the private part, for it is the place of filth and najis. 
According to the above discussion, in our opinion, touching private parts with the right hand is makruh tanzih and not prohibited. It is included in matters of manners and the restriction in the hadith is a form of guidance and education. Likewise, the act of holding the penis or private parts with the right hand is considered contradictory with honouring the right due to the fact that private parts are where the filth and hadas happen.
May Allah SWT grant us all a clear understanding in religion. Amin.