I definitely come down on the side of option A. Common names that are required to be (and remain) taxonomically accurate are not common names, they are non-Latinized scientific names. They are maintained exclusively by scientists, not inclusively by the “common folk” (meaning all of us). More on my opinions here.
That said, if there are particular taxonomic groups with well-established, rules-based English scientific names (or in other languages), and those taxonomists insist that those names should be the language default(s) on iNaturalist, that seems like something that could be discussed and, if agreed, added to the Curator Guide, so as to avoid “common name wars” in iNaturalist.