All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The dead Muslim has the right on his Muslim brothers that they wash him, enshroud him, perform the funeral prayer on him, and bury him, and it is not permissible for them to enable his non-Muslim family to prepare his burial according to the non-Muslim rites.
Preparing the dead body of a Muslim by washing him, enshrouding him, performing the funeral prayer on him, and burying him is a communal obligation regardless of whether the dead person had left a Wasiyyah (a will) to this effect or not. If none of the Muslims does that while they know, then they are all sinful.
Imaam An-Nawawi said, “Washing the dead, enshrouding him, performing the funeral prayer on him, and burying him are communal obligations without any difference of opinion among the scholars...”
He also said, “The meaning of communal obligation is that if a sufficient number of people do it, then the rest are exempted from sin, but if all of them do not do it, then they are all sinful...”
According to the view of the majority of the scholars, it is not acceptable that the Muslim's non-Muslim family washes him, contrary to the view of the Shaafi'i School, which states that it is permissible but disliked.
The Fiqh Encyclopedia reads:
“A non-Muslim washing a Muslim: The Hanafi and Maaliki Schools, as well as the Shaafi'i School in one of its views that is not the adopted view, as well as the Hanbali School, held that it is not acceptable for a non-Muslim to wash a Muslim because washing is an act of worship, and the non-Muslim is not eligible for it; so it is not acceptable for him to wash a Muslim, just like an insane person. Also, the intention is obligatory in washing, and the non-Muslim is not eligible for it, but the correct view of the Shaafi'i School is that if a non-Muslim washes a Muslim, it is sufficient.”
Therefore, if the non-Muslims among his family insist to prepare his funeral according to non-Muslim rites, then the Muslims have to make every effort to prevent it, especially given that he had written a will because the will of the deceased is binding according to the law, so they should take the matter to the authorities to oblige his family to fulfill his will that the Muslims take up the matter of preparing his funeral and burying him.
Allaah knows best.