Arguably; the 2010's are the first decade I've maybe seen without a serious incident like this I can recall, what with Eminem (and a lot of other rappers) firmly occupying the 00's.
1990's had artists such as Nirvana, Marylin Manson, and the turn of the 90's featured the controversy of N.W.A., Ice Cube, etc.
The 1980's, before the rise of rap in the late 80's; featured the metal movement, with often overtly Satanic lyrics and imagery such as inverted pentagrams. Christians would often gather and burn albums by Metallica, Alice Cooper, etc.
The 1970's continued the themes of psychedelia and occultism that first occurred in the 1960's, and albums by artists like Pink Floyd, Led Zeppelin and (introducing!) Black Sabbath, were; again - super controversial, not to mention the burgeoning punk scene.
The 1960's turned rock and roll into just rock; and you bet your ass those Beatles worshipped Satan, don't ya know! The 'bigger than Jesus' comment would remain in music history forever. The Beatniks and their pill-popping would raise eyebrows all over the world.
The 1950's featured the hip-swinging movements of Elvis Presley, who was certainly corrupting the youth of the time, infusing them with ideas of promiscuous behaviour. :O
That's probably about where I lose the plot, myself. I know jazz was controversial, but I don't know enough about the specific history around it beyond the obvious racial implications.
So you can certainly go back more than 50 years and find one or more of these 'controversy-mongerers' every decade for sure. :)
Outrage has always sold. Outrage goes Platinum. ;)