Alice Cooper is a born-again Christian man. I don't know for sure about Ted Nugent but if I had to guess, he's Christian, or at least was raised Christian.
Christ is a powerful steadying force. The fact that these guys act up on stage has little to do with their real inner self.
Cooper, born in Detroit, is the son and grandson of preacher men. Church of Jesus Christ.
Ted is Straight Edge if you know what that means.