The wiki is definitely not the place for tagging questions, please use either an appropriate mailing list, the help site or one of the forums (the later will be migrated here later in May). See also Welcome to Wikipedia users - OpenStreetMap Wiki
Nearly always the best way to start answering queries like this is to use taginfo to see what current usage might be. There are 26 craft=cider and 8 craft=cidery.
In general it’s worth sticking with the most popular value, and in this case I don’t think there’s much ambiguity. “cidery” itself may not be universal usage, for instance it is apparently not accepted as a word by scrabble.
Thanks, I’ve just remembered that the wiki search doesn’t include talk pages as default, and I was so intent on using this new forum that I didn’t check manually!
I can’t believe that, as a very long time Wikipedia editor and kinda long time OSM editor, I’d never seen that page before! (I’d picked up most of it over the years but always thought talk pages were the place to talk, until now!)
frankly, I don’t like neither craft=cider nor craft=cidery. The way “craft” was conceived, a typical value should describe the profession of the people who work there, e.g. craft=carpenter hence the value here would be something like craft=brewer or maybe very specifically craft=cider_brewer
I have to acknowledge though, that somehow the craft tag was “invaded” with other values similar to the ones discussed here, in particular frequently used grinding_mill, winery and brewery all follow the cidery/cider scheme as well. Looking at these, I would guess a place producing cider is a “brewery”, not?