I care. No matter how it happened, the response should have been A) "It was wrong", B) "I've apologized by phone with them". and C) "We've taken steps to ensure it doesn't happen again". In that order. Looks very unprofessional and gives fuel to the opposition.
I see it as a slip up by someone, including Trump. One slip is forgiveable, two? Not to much.... And No, I don't think the mexican moustache and sombrero with "La Cucaracha" song was racist.