In the '50s drugs were still a cultural taboo by broadcast standards. The radio shows of the time still primarily used the term "narcotics" to describe just about any illegal drug. This changed with the surging popularity of Dragnet. Jack Webb was staunchly for accuracy in his police procedural, so with it's rise, so too came the individual drug names (heroin, marijuana, amphetamines) as well as the colorful nicknames. (smack, reefer, goofballs, bennies, reds, etc)

As far as the musicians of the day, in the early '30s, while marijuana and opium use was well known in the jazz community, it was still a public relations scandal if the drug use became public or made the papers. By the '50s, heroin and cocaine use was exploding in those same communities, while marijuana was leaving the ghetto and starting to enter mainstream society.

Musicians who were arrested for drugs had serious damage done to their careers. They were easy targets for police and were arrested with such regularity that the federal government set up what was known as The Narcotic Farm or "The Narco" in 1935 as an experimental treatment and research facility; a place to house drug offenders and research the cure for addiction. You can read about that in Nancy Campbell's book The Narcotic Farm: The Rise and Fall of America’s First Prison for Drug Addicts The place became an unofficial Mecca for addicted musicians and supposedly there were some legendary jam sessions played at The Narco.

As far as influence goes, that depends on where you were in society. For those who traveled with or hung out in the jazz scene, drugs were rampant. Absolutely rampant. Some of the big names who were either addicts or caught in a drug scandal were Ray Charles, Johnny Cash, Billie Holiday, Miles Davis, Charlie Parker, Cab Calloway, Gene Krupa, and Thelonious Monk to name a few. All of them revived their careers and had success but there were many lesser known musicians whos careers were ended.

If you were not "in" the communities, then you either didn't know or only had gossip, rumors, and the occasional news story to go on. The radio broadcasters would simply stop playing the records and mentioning the artist until they were forgotten by the public.