Offering condolences to a non-Muslim on the death of a relative
Question

Is it permissible for a Muslim to offer condolences to a non-Muslim if his father or mother or one of his relatives dies, if there is a fear that if he does not go to them, they may harm him or it may be a reason of their being put off Islam, or not?.
Praise be to Allah.If the aim in offering condolences is to make them think favourably of Islam, then that is permissible and this is one of the aims of sharee’ah. The same applies if doing so will ward off their harm from him or from the Muslims, because a small infraction may be overlooked if that may serve the general interests of Islam. 
And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and Companions. End quote.