I’ll say I think ignoring the birther movement did the most damage, but not really. I’ll explain.
Natural Born Citizen had a pretty clear definition, which both candidates failed for opposite reasons. Obama failed the original definition because both his parents were not US citizens. McCain failed because he was born on Panama soil and from my understanding of it there was no military hospital the year he was born, though a year or two later he was issued a birth certificate from the then new base hospital.
I say “but not really” damaging because I think the NBC requirement needs to be revised. It made sense in an age when being born someplace generally indicated that you would spend a significant part of your life there. Same with parentage. In today’s age I think “citizen at birth” is a fine requirement, which both met, and not the more stringent original definition of Natural Born Citizen.
The only reason I do think it was damaging was because it effectively changed the requirement for the office by ignoring it, rather than actually changing the requirement.