Surely Billy Holiday had some influence on public attitudes to race in the USA? And surely that influence would have been lessened without the song "Strange Fruit"?

OK, so that's only part of one person's influence. There are many other songs that sustained a movement (the Marseillaise, early Negro Spirituals, "We Will Overcome", The Manchester Rambler, etc). For a really decisive influence, I'll quote from a scholarly article (http://www.tandfonline.com/doi/abs/10.1080/01411897908574506, of which I'll admit I've read only the free sample):

It is accepted as a fact of musical history that a performance in Brussels on the 25th of August, 1830, of Auber's opera, "La Muette de Portici", precipitated the revolution which led, eventually, to the establishment of Belgium as an independent nation.