I’m not finding the body class on the homepage to be blank. The classes that are present depend on whether or not there is a logged in user, but either the class navigation-categories or the class navigation-topics should be present.
If your homepage is displaying categories, you may be able to target that page with .navigation-categories. If your homepage is displaying the latest topics, targeting it with CSS may be difficult, because navigation-topics will appear on the latest, top, and unread pages.