Is it permissible for a Muslim to participate in the burial and mourning rituals of non-Muslims that include polytheistic practices such as bowing to the deceased and offering incense? Is a Muslim sinful for participating even if he does not believe in those actions? Is it permissible to allow a Muslim wife to attend such rituals in the future?

It is permissible to offer condolences to a disbeliever if there is an overriding benefit in doing so, such as inviting them to Islam or averting their harm from Muslims. This applies equally to relatives and non-relatives. However, attending the funeral of a disbeliever is not permissible, because it is a form of glorifying the disbeliever. Likewise, it is not permissible to shake hands with non-mahram (definition) women, whether directly or from behind a barrier, due to the risk of temptation involved.