How can one deal with family members who possess varying degrees of faith, what is the definition of an apostate, and is it permissible to bury someone who does not believe in the Islamic religion in Muslim cemeteries?

An apostate is one who, after embracing Islam, commits an act, expresses a saying, or holds a belief that the Divine Law has indicated to be an act of disbelief (kufr), whether they were raised in a Muslim family or not. Thus, denying the Messenger, or hating and insulting him, constitutes disbelief. Likewise, doubting what has been established from the two revelations (Quran and Sunnah) is disbelief.

A servant cannot be a believer except with absolute certainty, but they may experience a doubt that does not expel them from faith.

Declaring specific individuals who ascribe to Islam as disbelievers is not a light matter. An individual is not judged to be a disbeliever except after all conditions are met and all impediments are absent, such as being an adult, sane, intentional, acting by choice, and not excused by ignorance or misinterpretation.

The judgment against an apostate and the execution of the punishment are entrusted to the Sharia judiciary and the ruler (wali al-amr).

Filial piety is obligatory, even if the parents are disbelievers, but there is no obedience to a creature in disobedience to the Creator.

It is obligatory to submit to the rulings of the Divine Law, and disliking the rulings of the religion is a sign of disbelief.

It is permissible for a Muslim to follow the funeral procession of a disbelieving relative and bury them. However, an apostate who has been officially judged to be a disbeliever is not to be buried in Muslim cemeteries.

Abandoning prayer is the gravest sin after shirk (associating partners with God), and it is a distinct sign differentiating between a Muslim and a disbeliever.

One should strive to guide those who have deviated with patience and counsel, using wisdom and good admonition, focusing on strengthening faith, rectifying hearts, and teaching the legal rulings.