It depends on the level of SHTF. Morality is important if you're in an anarchic society that revolves around community, and I'd like to think that's where we'd be. On the other hand, if it's every-man-for-himself, well then the survivors will be those who have no morality.

Personally, I'd bank on community. If it's EMFH, I'd rather die sooner than later, as it wouldn't be a very nice world to live in at all. At least with community, life is still enjoyable.