It is not fair to blame them, nor is it fair to give them what they want automatically. The situation may be aggravated because modern people are used to controlling their entertainment. They want to change the channel and change the station or the CD, and they want to change your channel if you are the musician. It is hard to know if people were different a hundred years ago when the musicians did not have knobs and remote controls. They honestly cannot help themselves.
Comedy often works.
So does playing 15 seconds of the song and then apologizing because you don't know it all. Sometimes all they want is acknowledgement of their interest to show that they like you. If they want to hear On the Road Again, mention that it is a Willie Nelson tune and talk about Willie and how much you like him, and then play something else by Willie. Or else play one of your own songs and lie and say it is a Willie Nelson song. Learning or writing a parody of the song they want to hear is a good way to straddle the fence.