I think you need to get some clarification from your religion. What is "death"? There are plenty of patients who will "core" - i.e. die - who will need CPR, intubation, drugs, etc. before they are fully pronounced "dead". And yet they have no heartbeat, no respirations while they are worked on. And what if a child comes into the ED with cold water drowning? No heartbeat, no respirations, but the rule is you work them until they are warm and dead. And what about cardiac surgery where the patient is on bypass? Heart not beating.. full life support. Is that patient "dead" in your religion?
If you can't do those things because the patient is "dead" then perhaps medicine isn't for you. You would not be able to fully participate in an ICU rotation, an ED rotation, perhaps even a surgery rotation, an IM rotation... you would have to go to a rotation site and a school willing to work with you on this restriction.
And if you can't have contact with any dead body, what about prosections? They're still dead. you have to identify parts. I could see this being avoided if the med school was willing to take pictures and have you do a picture exam, but this might be exceedingly difficult depending on the picture they give you.
I'm not trying to be a jerk or dissuade you, but rather bringing situations to your attention to reconsider whether you can indeed go through medical school with your particular restrictions, and that you may have to contact each medical school you wish to apply to in order to see if appropriate accomodations can be made.