If I am using the barb camp as a "culture farm" I will immediately kill any scout that comes near. I also immediately, and without reservation, kill any missionary or prophet that I see in my territory. Most of the time, my defenses are up to the task of repelling the AI invasions. In those rare cases where an AI has a massive military that sweeps me into the ocean like one would casually flick a bug off one's arm, I accept my defeat and move on to the next game.
Edit: OK, OK! I accept my defeat AFTER I run screaming around the house, throw various small, breakable objects around, and curse the universe for allowing me to loose....