I think that the censorship of lyrics has occurred with radio consolidation in the 1990s.
It might have had some effect, but I think the ebbs and flows of moral conservatism have always been a bigger factor on a local basis. Sometimes that local outcry spread enough that it effected change for all stations in a region and in some cases it became a nationwide movement. But you make an interesting point about the factors that may have influenced censorship. Of course it's been around a long time; for instance with a couple of '60's songs that you might hear on oldies stations. The spoken lyrics at the end of Jimmy Dean's "Big John" were changed from "...one hell of a man" to "...a big, big man." The Swingin' Medallions "Double Shot of My Baby's Love" fell victim, too. "Worst hangover I ever had" became "worst morning after I ever had." Those changes happened relatively shortly after the songs were released. Then again, there have been numerous songs that have been banned altogether throughout the history of the medium, although generally on an individual station basis, and usually following community pressure. One comes to mind in the pop music field: at one time some radio stations didn't give airplay to (or stopped playing) the Strawberries' "Go All the Way." Awfully tame stuff compared to what we've heard for the past couple of decades.