MY LUNCH, MY TIME!
End of story. I don't care if one of the two who walked up to me during lunch was Jesus Christ with the cross on his back and the other was Barack Obama. If it were I'd invite them to join me for lunch. Any other person, If it were me, I'd have had two very large "Security Men" present and the two activists after being politely being asked to wait until I finished lunch would have left, either voluntarily or otherwise. In good health or otherwise
Maybe I will be in public office? I have been asked to consider a run by two people in my area. I have the right to conduct myself as I choose. If I ever did run I'd make it common knowledge that you don't bother him when he's eating, PERIOD!