The story
From Bakunin + -ist. In regards of the alternative form, as the -ин (-in) suffix in Баку́нин (Bakúnin) is dropped in Slavic under various conditions, the name for the ideology, its adherents and the relative adjective also appears without it translingually for euphonic reasons, following particularly strong tendency to omit it in Slavic languages, so that the longer form does not even exist in Russian.
Etymology from Wiktionary, CC BY-SA 4.0.