My code analysis does show an issue with permissions for editing tags, but by your screenshot it seems like it is different from what you are experiencing. Please double check that your "Characters" area does not have custom permissions for any of the affected groups, and if it does, that "Can tag wiki pages?" in that area still reflects your expected permissions.
The issue I found is that a user with "Can tag wiki pages?" will still see the link to edit tags, but when clicking on it, may receive a rejection message saying they don't have proper permissions to do so. It sounds like you are seeing a different effect; please confirm.