I don�t think the acceptance or disapproval of euthanasia in society hinges on religious belief, although people often refer to it as �playing God� or life belongs to God etc., it has more to do with social attitudes and the acceptance of the power of one to take another�s life. In the right circumstances most people would wish for a dignified death (providing they knew that death was impending of course!), the problems become apparent when it requires someone else to help or assist with the death. Some medical practitioners and individuals would prefer not to have that responsibility.
In olden times, a warrior would die a �good death� if he died on the battlefield with sword in hand � and this often has religious connotations in that the warrior (depending on the base belief) will join his ancestors in a great place reserved for worshipful heroes. Even on occasions where a warrior-type was executed, out of respect, he would often be allowed to be grasping his sword at the point of death, if not he believed that he would most likely be left wandering the underworld in shame.
Killing yourself because you are tired of pain or embarrassed by disability is the exact opposite of what you are asking. It is taking your life not so that others won't suffer, but so that you won't suffer. In comparison, you could consider the fireman who enters a burning building to help other�s escape, or the doctor who treats terminally diseased people knowing potentially they could contract the disease and also die. It is with this act of servitude and self sacrifice that the crucifixion of Christ is viewed, not as euthanasia.