No the government/radio should not be able to censor lyrics. Its part of the first amendment. Artists write the song the way they feel, I know form experience because I'm a singer/song writer. The artist produces the song to give people a glimpse of how they feel deep down. What do you think???
The government should not be allowed to censor anything as it is our freedom of speech to say whatever we think or feel, even if it is vulgar. Rap does have a lot of violent and or expletive lyrics to it, but freedom of speech is exactly what gives them the right to say it, and censoring it is not constitutional.
The government should never be in a position to censor speech, no matter how hateful or disgusting that speech may be. If someone finds gangsta rap offensive, they need to choose not to listen to it and allow those that do enjoy it to continue listening. Violence and expletives do have a place in artistic expression, and if we allow censorship of one form of expression, everything else becomes at risk.