Genre, Fanfic, and Community

Fanfic is generally considered to be belonging to the science fiction community, yet there is an enormous history of non-SFF works that lead to fanfiction (Starsky and Hutch being one of the first television shows to yield a popular slash pairing). Then of course there is SFF property that is recreated by fans within non-genre settings (unless the coffee shop trope counts as genre). What is the relationship between genre, fanfic and community?