Is it permissible to perform the funeral prayer (Salat al-Janazah) upon adherents of extreme deviant sects like the Jahmiyyah or Rawafidh (Shi'a)?

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Imam Ahmad stated that he does not perform the funeral prayer for the Jahmiyyah or the Rawafidh, permitting whomever else chooses to pray for them. This position is supported by the precedent that the Prophet (peace be upon him) abandoned the prayer for offenses lesser than this, such as religious deviation, treachery (ghulul), or internal struggle. Imam Ahmad explicitly stated that the Rawafidhi is not prayed over. Abu Bakr ibn Ayyash concurred, stating he would not pray over a Rawafidhi or a Kharijite. Al-Firyabi declared that whoever insults Abu Bakr is an unbeliever and should not be prayed over. When questioned about such an individual despite their utterance of 'La ilaha illa Allah,' the response was to handle the body using wood and avoid touching it directly until it is buried.