It's worth noting that until around the 1950s the dangerous effects of smoking tobacco were not widely known, or at least not considered proven. It was actually considered quite good for you in some circles and prescribed as a cure for throat and lung complaints. It wasn't until 1954 that the British Doctors Study confirmed a link between smoking and cancer and people started to take notice.

Tobacco and a pipe don't weigh very much, even if you're taking a considerable supply. I'm not terribly well read on Shackleton but from what I can find out he seems to have thought he could make the crossing in a single season over the winter. Given that the plan was to mount an earlier expedition to leave supply depots along the route I imagine the extra weight of tobacco and smoking equipment was considered negligible compared to the morale and (as far as they knew) health benefits of taking it along.