"not wanting to take on some fucking responsibility for others."
They'll have to explain their sins themselves, but by observation I think its giving up that they oppose.
Going up to OPs question of who gets to decide, decades ago when my father died of some weird fast moving liver cancer no one religious had any issue with the numerous treatment options all somewhat fatal or with the concept of being able to select a treatment plan. So the oncologist says chemo option A means X amount of pain and 90% chance you'll be dead in Y months, and option B, C, D, all different tradeoffs, or we could try whatever else and you'll get Y months with X amount of pain, or do nothing and you'll be gone in about Y weeks or etc etc. Basically the patient and team of doctors pick a death date which results in an associated level of pain and medical treatment (medical profit). The Christians don't seem to mind "pick a death date" they just seem very unhappy with the idea of the treatment plan being "give up completely" "game over".
There seems this weird assumption that people can't handle picking a death date or it would warp culture too much, but any cancer patient with more than one medically approved treatment option is pretty much picking their date as it is today. Especially if its terminal cancer. Adding a third, fourth, fifth treatment option of "once we agree your quality of life is below level X then you're done" isn't going to be a huge addition or huge problem.
My wife has power of attorney or whatever its called over her Alzheimer's damaged great uncle, she has full control over all of his medical treatment plan. The only real moral or ethical argument I can think of is if it were made legal maybe only only legal agreements drafted after the law change should be valid. Although then again, the whole point of her being in charge is he trusted his niece the most so if he were competent he would likely continue to trust her the most anyway.