Is it a sin for a female member and moderator to remain in a translated anime forum that contains inappropriate clips and music, while she also supervises the Islamic section and fears losing the reward of benefiting and imparting knowledge to the members if she leaves the forum? And must she leave the forum?

It is not permissible to watch or disseminate animated films that contain unlawful elements. If the forum where you oversee the Islamic section is based on a forbidden activity, you must declare the impermissibility of these films and advise users not to watch or translate them. If you remain in your supervisory role with this declaration, there is no sin upon you for staying while continuing to offer advice. Otherwise, you have fulfilled your obligation.