Sadly, the first song that came into my head that was banned was Yankee Dollar by the Andrews Sisters for mentioning Coca-Cola.
Not quite a ban as such, more censorship, but Elvis was forced to sing Hound Dog to an actual dog on a table so that viewers couldn’t see him from the waist down...something that must have riled him as he frequently mentioned it in his ‘drugged up in Vegas’ period.
Anyway, to regain some musical credibility, I’m pretty sure this has been banned in it’s time.