I agree with Mangoey, in your case it was just a mean customer who refused to be human about it. Everyone makes mistakes and it´s not like you had hurt the dog or anything. A bit of understanding and compassion and things could be fine. Of course when I pay for something I would be glad to receive an appropriate service, but I can also be understanding about small mistakes, especially when I can see people are honestly sorry about making them. She was just being dumb. Maybe she had a terrible day herself? or someone was stepping on her toes in her own job, so she was just taking that on you, which is unfair but that is how I often feel people carry themselves.
As for your question. I think it depends on who is giving the criticism and how. When it is a person I respect and who I know is really good at their field, I am very open to it and I see it as a way to improve myself. When I´m not being yelled at and kindly explained the pros and cons of my work, that´s awesome. Make me better, I want to be amazing :D. But when it´s someone who I just don´t vibe with in general, I don´t respond well. I immediately become defensive and I can get bitter. It´s not a good personality trait, I´m the first to admit, but not everyone is entitled to criticise :D.
I appreciate when people tell me beforehand like "May I offer some advice.... or ... Is it ok to tell you that ..." so that I can prepare and calm myself down. I tend to take things less personally afterwards. I take criticism of my work better because I work with people and I understand that knowing what bugs them might actually help me in the future, but I don´t like when people want to offer their criticism on my life or looks. I find that unnecessary and it just makes me angry because my general opinion is "live and let live".