If it's constructive criticism, I won't be bothered by it. After all the person is taking time to help improve my site! Now if the person is being disrespectful and won't explain why they say negative things about my site, I wouldn't be too happy about it. I wouldn't be too offended however, I would ask them what they don't like about my site. If they keep saying things that aren't constructive, I'll just ignore them.
I've had a user or two post their negative views about my forum at one point. I remember one person posted their criticism on a blog. I was deeply offended at the time and even counter-attacked them with my own opinion. But this was in my teenage years, when everything offended me. Nowadays, if someone were to criticise my site, I would either see it as room for improvement or disregard their opinion.
Every criticism is a feedback, even if I don’t like the tone it was conveyed. I will filter out what I need and just discard the rest, I don’t let peoples choice of words online get to me.