Is it permissible to pray behind a father who believes in the obligation of following the hadiths that explain matters in the Quran, to the exclusion of hadiths that mention matters not mentioned therein? And if it is not permissible, is it then permissible to feign praying with him and then repeat the prayer?

Patience and gentleness in advising a misguided father are obligatory, along with acknowledging his virtues. The story of Abraham (peace be upon him) with his father can be used as an example of gentleness and good manners.

If the father's innovation (bid'ah) takes him out of Islam, such as completely denying the Sunnah after proof has been established, then prayer behind him is not valid. However, if his innovation does not reach the level of disbelief, such as his failure to adhere to some Sunnahs due to negligence, then prayer behind him is valid.

If his denial is a denial of rejection (juhood), then he is a disbeliever (kafir) and an apostate (murtad), and it is not permissible to pray behind him. If his denial is an interpretation that is permissible (ta'weel sa'igh), then he does not become a disbeliever, and prayer behind him is valid, unless there is a benefit in refraining from praying behind him so that he may be deterred. His denial of anything beyond the Quran is considered a great innovation.