There was a time when Jazz was not fancy, there was a time when it was considered a corrupting influence. It was linked to crime, drugs, insanity, promiscuity...

Check this article published in Ladies Home Journal, August 1921.

Racism was obviously a component in the prejudice against that music (and some others that were put in the same category).

Basic popularity eras:

1896-1912 Ragtime Era

This is when rag was at its peak. They were using it even in London (The Nightside of London), though not where High Society gathered.

1912-1919 Tango Era

This is the time when tango was the new thing (1912 in America debuted the fame of the Titanic, Tarzan & tango). It was racy and radical. It continued to be danced into the 1920s, but it wasn't rebellious then.

1919-1934 Hot Jazz Era

Jazz went from the underground to the inescapable, especially it was promulgated by radio. That eventually sent it into every corner of the land, much to the horror of conservative parents. There were many levels and flavours of jazz. It was majorly popularized by Paul Whiteman and his orchestra. Interestingly, in his first autobio Rudy Vallée says Whiteman didn't play real jazz, just "syncopated orchestral music." He didn't claim to do real jazz himself, but most of us use "jazz" more inclusively.

1934-1944 Swing Era

I date this from when Benny Goodman broke big as a national phenomenon. Musical styles are always in existence before they get out of very small circles of listeners. In swing there was sweet swing and hot swing. Your parents wouldn't object to a sweet swing band like Guy Lombardo.

1944-1954 Cool Jazz Era

Its like WW2 broke down and tired out bands. That and anyone gets bored doing the same thing. Still, Goodman did say later that be-bop was a mistake.

1954-1964 Rock'n'roll Era

I don't have to tell you about this.

Notice that except the Argentine tango, all this sound originated in American black music. Rock'n'roll came out of country swing, but that came out of country , blues & swing. But we also need to note that they break big after they begin being taken up by white or mixed bands. It took Elvis to take rock out of "race music." Same thing with forms of jazz, to move it out of small markets.

In Europe, this is in spades. The jazz is uncultured American, as well as black. This makes it even racier and more rebellious.

In fascist Europe, kids who took up swing usually did so via its British forms and recordings. It became very serious rebellion, actual resistance, in Nazi Germany and occupied France. Savage' Teenage: The Prehistory of Youth Culture: 1875-1945 has chapters on this.

I would have to dig out my textbook from the History of Rock n' roll class I took in college to provide a proper reference, but I can provide some insight to controversial music of the past.

Before rock n' roll you had classical, big band and country considered to be "white" music. These were commonly excepted by the white population. Swing music is a style of big band that the kids like to listen to, but it was not controversial in the US. It was in Germany, because Germany was trying to prevent American culture from seeping in. On the other hand you had jazz, soul, gospel and blues to be considered "black" music. Blues was specifically controversial, because this came from the growth of what was called field hollars (songs slaves sang in the fields to express their strife).

Rock n' roll had a particular distaste in the white community, because white kids started mixing country and blues together. Country was the rock and blues was the roll. Actually though, sciffle began to develop before rock n' roll. Sciffle was the concept of making musical arrangements with nontraditional assembly of instruments. Some of these bands were considered jug band. The Beatles actually were a sciffle band before their arrangement of drums, guitar, bass and keyboard became widely utilized in rock n' roll.

Long story short the music that was controversial in the US were genres that either we're conceived or inspired by black culture.