He never held the microphone close to his mouth, so I imagine he took the shoes off so that he would not make so much noise during the presentation.

So he does not damage the floor of the stage.

Why was he taking questions at an orchestra performance? As far as I know he is a former active scientist and now a half baked celebrity. I didn't know he played an instrument to that level? Or was he conducting. 

Neil deGrasse Tyson listening to an audience member's question last night at the Boston Symphony Orchestra