Is it permissible for a Muslim father to shelter and provide for his atheist son, and is it permissible for a Muslim son to live off his atheist father's money?

It is not permissible to be lenient in judging someone as an unbeliever or an atheist; rather, one must invite him to Allah. Financial support (nafaqa) is obligatory for a poor parent from his child's wealth, even if the parent is a disbeliever, and vice versa. Our muftis hold that a Muslim father is obligated to provide for his disbelieving son, and vice versa, if the disbelief is original (i.e., not apostasy). However, financial support is not obligatory for an apostate because his blood is considered forfeited. Yet, if there is a benefit in providing for him, such as winning over his heart, then that is good. It is permissible for a Muslim child to benefit from the wealth of his apostate father if the child is poor.