"Elitist" has been a very generic and broad term to generalise many types of not-so-mainstream or "deep" anime, so this list is very diverse and it's criteria are not always clear cut and objective. Nonetheless I try to provide a proper explanation for why each entry is included. Generally speaking these are shows that fit one OR more of these adjectives: Experimental, Avant-Garde, Psychological, Philosophical, Obscure, Classic, Critically Acclaimed, Artsy, Old, etc...
Some shows here are not necessarily obscure or underground at all, but they are still here because they have been stereotyped as "elitist" by the community over time, due to their experimental or artsy nature. Similarly, some shows here are not necessarily artsy or experimental in nature, but their old/underwatched/obscure nature gives them a reason to be here. Not all aspects have to be checked to be included. Only one per franchise.
I have personally watched the great majority of the anime in this list, but there are a couple which I haven't. Still added them because of how strongly they are stereotyped as "elitist" or have fitting characteristics to be classified as such. I know my list still lacks many essential classics, I will continue to add and expand into this list as I watch those personally.
For more recommendations, go to my other Interest Stacks, "Elitist Anime 2" , "Elitist Anime 3" and "Elitist Anime 4", whose links are:
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Anilist Sync