Is it permissible to perform funeral prayer over those who hold severe deviant beliefs such as denying the Caliphate of 'Umar or condemning prominent companions?

Primary text

Abu Bakr ibn 'Ayyash ruled that the funeral prayer is not performed for a Rafidi because he claimed that 'Umar was an unbeliever, nor for a Haruri because he claimed that 'Ali was an unbeliever. Al-Firyabi stated that whoever curses Abu Bakr is an unbeliever and should not have the funeral prayer performed over him. The justification for omitting the prayer for such individuals is that they declare mainstream Muslims to be disbelievers and do not offer prayer for them, thus they are treated as disbelievers, whether they are Dhimmi or otherwise. Alternatively, it is argued that they have defected from the religion, making them similar to apostates.