Have You Ever Blocked Someone?

Okay, I told myself that I would never block anyone on here because everyone's entitled to their own opinion. I try to be polite to everyone, even those with differing views from me. When they push an issue too much, I tell them I'm sorry but I'm not interested and wish them luck in finding someone else to chat with.
But what do you do if they keep at it? Ignore them? Block them? I feel bad, because I know they desperately want someone to talk with, but...