Most of them do, however they disagree in a lot of different and often entirely contradictory ways.
So given the problem of doing something about a disaster, trying to keep all the different belief systems happy at the same time will just stop you from doing anything. You can't keep all the different belief systems happy when there isn't a disaster and lives to save, trying to do it when there is seems to be just setting yourself up to fail from the outset.
Also, given the context of disease, stopping it spreading is not a wholly altruistic act. This is about self-preservation as much as anything else and most of the world's religions are pretty clear on what you are allowed to do to others when the tribe is threatened. The religious reaction to this in many cases would be mass slaughter.
So given the problem of doing something about a disaster, trying to keep all the different belief systems happy at the same time will just stop you from doing anything. You can't keep all the different belief systems happy when there isn't a disaster and lives to save, trying to do it when there is seems to be just setting yourself up to fail from the outset.
Also, given the context of disease, stopping it spreading is not a wholly altruistic act. This is about self-preservation as much as anything else and most of the world's religions are pretty clear on what you are allowed to do to others when the tribe is threatened. The religious reaction to this in many cases would be mass slaughter.