I had a bit more of a look into it and it didn't get any clearer 😕. The original prohibition was against "hot drinks", which was later clarified to mean coffee ☕ and tea 🍵. Modern Mormons apparently argue over the whole issue. Some won't drink caffeinated beverages of any sort, some probably don't drink decaf, others do.
It can be a problem when a founder creates an immutable law that doesn't make sense as society progresses. The SDAs probably find it with some of White's "revelations". The whole vegetarian thing was founded on the belief that a meat rich diet made one strong and virile, and it also provided fuel for the baser passions. Their vegetarian diet was deliberately intended to make people weaker, who would therefore have less energy to channel towards those baser passions.
Interestingly, defying the above rules would probably be seen as "following the world" by devout practitioners of the above faiths. And to an outsider, one who'd never been in, such a view would make as much sense as Rattigan's stance on Christmas lights.