Good News Week was "political" by 1964 standards -- "Someone's dropped a bomb somewhere contaminating atmosphere -- who won that race? What's the weather like today." They don't write them like that anymore. Then there was Jonathan King "Everyone's Gone To The Moon." Weird lyrics in that one too. Last I heard, he was serving time in prison for kiddie porn.
"Eve of Destruction" and the answer song "Dawn of Correction" also had political overtones.