You raise an interesting point here, not something I thought of right away. But think about other common genres.
What well-known genre hasn't invoked controversy and civil disobedience? The classical renaissance era. Jazz and ragtime. Rock-and-roll in the 50s. Psychedelic, pro-peace music in the 60s. Anti-establishment punk rock in the 70s and 80s. New-wave music, pioneered by Brian Eno, in the same decade. Hip-hop in the nineties.
Music is so fascinating, so vastly important, and so inherently controversial that you can hardly say a genre has caused more trouble than others. Not to mention that, in the case of early 20th century jazz and rnb, the controversy was not the music itself but that Black people were being heard and respected. White folks couldn't stand to see Black singers, especially Black women, pulling any kind of crowd.
As with all of those genres, the music itself is not responsible for controversy (well, maybe punk rock...) - it's an adversity towards change and progression in music.