If the inheritor and the one from whom he/she is inheriting are of different religions, then as per the Shariah, the inheritance laws don’t come into play at all. There is a Hadith in this regard:
It is narrated on the authority of Hadhrat Usama bin Zaid (May Allah be well pleased with him) that the Holy Prophet (Sallallahu alaihi wa sallam) said: A Muslim cannot be the heir of a non-Muslim and a non-Muslim cannot be the heir of a Muslim. (Sahih Muslim, Hadith No. 4225)
If the parents are non-Muslim, then as per the Shariah, Muslim children of those parents are not their heirs. As far as treatment of parents is concerned, even though they are non-Muslims, the parents should be treated honorably and kindly. They should be served. However, if they command any sin to that extent they should not be obeyed.
And Allah Most High knows best.
Mufti Hafidh Syed Ziauddin Naqshbandi Qadri
[Professor, Islamic Law, Jamia Nizamia,
Founder-Director, Abul Hasanaat Islamic Research Center]