I don't know all the details, just what I've heard some people involved share about it on various local podcasts like Desert Lady Diaries [3]. It sounds like a major objection is the presence of a Dollar General casts an area as impoverished, making it less attractive to potential transplants/investors/tourists. Joshua Tree residents and business owners are trying like hell to distinguish the area from its surroundings as a classy enclave full of artists, and want to do their best to attract the preferred kind of investment and residents, raising the bar - not lowering it.
It is quite visible when driving through the surrounding towns. The Dollar General stores, definitely leave a crappy impression. I visited one once just to see what they sold, and the sliced bread loaves on the shelves were moldy, some had insects visible inside. NOPE.
[1] https://www.facebook.com/groups/nodollargeneraljoshuatree/
[2] https://www.desertsun.com/story/news/2014/12/25/dollar-gener...
[3] https://www.youtube.com/channel/UCmGyfvro5aierNkIuSNVDOg/vid...