Complex sentence: Kuhač went on to claim that the reason Haydn used so many Croatian folk tunes in his music is that he was himself a member of the Croatian diaspora, and thus a native speaker of Croatian and a direct participant in Croatian folk culture.
Split into simpler sentences: Kuhač went on to claim that the reason Haydn used so many Croatian folk tunes in his music is that he was himself a Croatian; that is, a member of the Croatian diaspora. As such, he would have been a native speaker of Croatian and a participant in Croatian folk culture.