Determinism arguably does nullify moral responsibility, but that point is extremely limited in application. Moral responsibility is a construct that has been proven throughout time to be a way to give the best outcome for all parties involved in any given situation. Determinism is for the most part unfalsifiable, so its implications in practice are unclear.
I don’t think religious ideologies should be given any weight in this matter, since they are generally built on primitive traditions rather than reason or research.
@lucillelucillelucille That depends on how depressed you are, the way in which environmental factors have modified your reaction time, and whether your senses are able to detect the falling tree. Only a healthy, fully able and cognizant person will be certain to jump out the way.