The Questioner: Is the order in wuḍūʾ obligatory? And what is the evidence for that?
Shaykh Muqbil: The evidence for this is the statement of Allah, Exalted is He:
يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا قُمْتُمْ إِلَى ٱلصَّلَوٰةِ فَٱغْسِلُوا۟ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى ٱلْمَرَافِقِ وَٱمْسَحُوا۟ بِرُءُوسِكُمْ وَأَرْجُلَكُمْ إِلَى ٱلْكَعْبَيْنِ
O you who believe! When you intend to offer aṣ-Ṣalāh (the prayer), wash your faces and your hands (forearms) up to the elbows, wipe your heads, and wash your feet up to the ankles.
It is mentioned in Sībawayh, “They begin with that which is of greater importance and seriousness in its affair.” Likewise, the action of the Prophet ﷺ and his consistent adherence to making wuḍūʾ in the prescribed order; for it is not authentically established that the Prophet ﷺ ever made wuḍūʾ out of order.
And the Ḥanafīs have said that it is permissible [to not follow the exact order], but the Ḥanafīs’ opinion are not to be accepted nor are their statements depended on. Thus, the correct view is that observing the order [in which it was revealed] is obligatory, and al-wuḍūʾ is not valid nor accepted without it.
From the tape: Questions of the Women of al-Burayqah