We get the same thing. Being in a classic rock band, we always get far-out requests. I usually introduce the band as a "classic rock" band. The requests for Nirvana or foo fighters usually crack me up. I'm always honest & tell 'em "Sorry. We're a classic rock band. Those songs won't be classic to us in another 20 years"! They usually laugh it off.
"Good bands get requests.
Professionals should learn how to deal with them respectfully."
Very true. But how many of the BIG bands - y'know the ones whose songs we cover take requests? Out of all my 40 years of going to concerts only 1 - James Taylor listened to people make requests. And he told them he didn't take requests..