Is it permissible to host a friend who has apostatized from Islam in one's home?

There is no harm in hosting an apostate if there is a hoped-for benefit, and this is used to guide him towards good and away from his misconceptions. However, if abandonment is hoped to benefit him, then he should be abandoned.

Judging a person to be an apostate is not easy; for it is necessary that he must have done what necessitates it, that proof must be established against him, and that the conditions for excommunication are met and its impediments are absent. If he is judged an apostate, he is asked to repent; if he repents, then good, otherwise he is killed for his apostasy, based on the Prophet's (peace and blessings be upon him) saying: "Whoever changes his religion, kill him." No one carries out the punishment except the ruler.