It's a myth because below are the titles of 60s and 70s songs that have been banned even in Western countries because of moral, military, religious and political motivations. Even up till today some of these songs have not been played on certain broadcast stations.
There are definitely extremities in lyrics as Yoko Ono's *Open Your Box (1970) proves, but to ban **Tell Laura I Love Her (1960) is questionable.
Open./Open your cold feet,/Open, open,/Open, open, open, lets open, lets open the cities./Open the cities,/Open, open, open the world,/Open, lets open the world./Open, open, oooh/Open, open, ooh!"
**"No one knows what happened that day/Or how his car overturned in flames/But as they pulled him from the twisted wreck/With his dying breath, they heard him say/Tell Laura I love her/Tell Laura I need her/Tell Laura not to cry/My love for her will never die..."
Rolling Stones: Lets Spend The Night Together (1967) - sex?
Cliff Richard: Honky Tonk Angel (1973) - HTAngel = hooker
Adam Faith: Made You (1960) - sex
Paul McCarney n Wings: Hi Hi Hi (1972) - sex
Donna Summer: Love To Love You (1976) - breaths, groans
Yoko Ono Plastic Ono Band: Open Your Box (1970) - obvious
Paul McCartney: Give Ireland Back to the Irish (1972) - obvious
Johnny Horton: Battle of New Orleans (1959) - 'bloody British'
Ray Peterson: Tell Laura I Love Her (1960) - death
Mungo Jerry: Have A Whiff On Me (1971) - drugs
Lonnie Donegan: Digging My Potatoes (1971)
The Beatles: A Day In The Life (1967) - drugs
Rolling Stones: Stoned (1964) - drugs
Ten Years After: Good Morning Little Schoolgirl (1969) - sex
The Coasters: Charlie Brown (1959) - hooliganism, spitballs.
The Everly Brothers: Ebony Eyes (1961) - death
The Kinks: Lola (1970) - product advertising
The Beatles: Lucy In The Sky With Diamonds (1967) - drugs
The Four Aces: Stranger In Paradise (1953) - ?
Bobby Darin: Mack The Knife (1928) - gang violence