I ignore almost everyone when mining, but not so much with intent. Mining is incredibly boring, and I only have a single monitor display setup. So when I go mining or fishing, I pop in my 360 controller, set the option in the game to allow input in background, and bring up netflix, only having enough of the screen visible that I can see where my next node is.

I won't pay attention to chat, I'll mindlessly run from node to node, while most of my attention is on whatever series I'm currently watching.