For every one of us, death is the certain and mysterious conclusion of this life. When someone close dies, we are left bewildered and seeking. It is a warranted, if not certain, speculation that religion itself grew out of the recognition of the finality of death. In Neanderthal graves, anthropologists have found petrified remains of flowers. It appears that rituals about death are almost as old as death itself.
Religions offer different paths to reconcile the perplexities of death. Although dealing with the same overpowering phenomena, faiths are not uniform in their responses. Some of the traditions are compatible, and some not.
The unprecedented mixing of populations, both ethnic and religious, poses new challenges to those who wish to be both faithful and respectful. We cannot always honor the requests of others if they violate our core religious beliefs; but as the question implies, at such a delicate time we must be particularly careful.
It is nonetheless possible to maintain one's integrity and accommodate others who are not the same. With sensitivity, we should be able to make the experience meaningful to members of different faiths.
If a Jew dies and has non-Jewish family members, there is no reason why they may not be asked to participate in the ceremony. A non-Jew can deliver a eulogy, accompany a body to the grave, place earth on the coffin, stand while prayers are spoken, comfort the other members of the family, and so forth.
The difficult question arises concerning participation in the specifically religious part of the burial ceremony. Traditionally, only a Jew may recite the Kaddish, the mourning prayer. I think this may simply be explained by teaching that communities reserve certain obligations (and privileges) for their adherents. There is an entitlement to inclusion and a penalty for exclusion for every association, club, school, and religious community.
I am mystified why a member of one community is upset at being excluded from the rites of another community. Guests to my home may eat at my table, but they do not sleep in my bed. They may watch my television, but they may not make entries in my checkbook. We all reserve the right to control access to parts of our lives, our homes, and our communities.
Religious traditions are sacred to those who practice them. They are the proper arbiters of what may be done and what may not be done. To take offense is to selfishly elevate one's own sentiments above the collective beliefs and holy traditions of generations.
That same principle of respect should govern the conduct of a Jew at a Christian service. He too may deliver a eulogy and be a respectful observer of the traditions of another community. In accordance with a longstanding tradition, a Jew does not kneel during a service or recite hymns that contradict Jewish belief (for example, hymns that deify or supplicate Jesus).
Sometimes, the tone of the service will strike another as odd. There are traditions in which funerals are celebratory; others in which wailing and wild displays of grief are the norm. The great human rule of tolerance here applies: It is hard to feel the purpose and meaning of another tradition unless one is inside that tradition. Contempt or dismissal does not injure the tradition but mars the heart of the despiser.
Against our will, as the Talmud says, we are born, and against our will we die. This is the predestined human condition. The time in between those brackets of inevitability is under our control. Across religions, let us realize that we are dealing with the same inexplicable agenda of the universe. If we huddle together for warmth, perhaps we will find that the human heart need not be quite so cold.