So... is Shimoneta to Iu Gainen ga Sonzai Shinai Taikutsu na Sekai finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 19, 2015
Manga finished: February 18, 2016
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
In a future Japan where sexually explicit content is outlawed and heavily monitored, a high school student named Tanukichi Okuma enters a seemingly pure and regulated environment.
He hopes to get closer to his crush, the student council president Anna Nishikinomiya, but soon finds himself caught in a web of rebellion.
Tanukichi is unexpectedly recruited by Ayame Kajou, the student council vice-president who leads a secret organization dedicated to spreading "lewdness" to fight against the oppressive societal norms.
Forced to participate in increasingly outrageous acts of defiance, Tanukichi finds himself torn between his desire for Anna and his unexpected involvement in this underground movement aiming to dismantle the government's strict morality laws.
He now navigates the complex and absurd situation, balancing his personal feelings with the radical actions of his new comrades.