Euthanasia
Euthanasia: Quantity of Life people hate it, Quality of Life people don't love it but want to have the option if things come to that.
Much like abortion, euthanasia is an issue that highlights the dichotomy between these two fundamental views of ethical priorities. Most people support or oppose both and for similar reasons.
"Not all moral issues have the same moral weight as abortion and euthanasia. There may be legitimate diversity of opinion even among Catholics about waging war and applying the death penalty, but not... with regard to abortion and euthanasia." -Pope Benedict XVI
Many religions prioritize the reduction of suffering in the world as a primary goal. Modern medicine has provided many ways to extend life, but often that means the prolonging of suffering. If the only outcome of life extension is suffering, then it's both bad religion and bad utilitarianism.
Traditional ethics was developed in a different time, where the extended prolonging of suffering through medical intervention was not a possibility. Nor did people have the ability to offer a significantly better childhood experience with family planning. Changing consequences due to technology changes the moral considerations. In situations like this, utilitarianism self-corrects where deontology dies in dogma.
See also: Longevity, Death, Death penalty