Most people say nice things and we just say a polite thank you and move on. I sometimes feel a little weird saying thank you on my kid's behalf, but she's too young to field these comments on her own and I'm trying to show her how to gracefully accept a compliment without making a huge deal of it, and this is the easiest way.
The only time it annoys is when people want to lecture or give advice or something. Sometimes I get strangers who want to admonish me to be careful with sunscreen or who have these ideas about what red hair "means" about personality, and I cut those conversations short and will walk away from someone who is being rude. When she was a baby I'd get people coming up and saying "this is very lucky, do you know how lucky you are?" and it was kind of weird because it would start out with me saying "oh, thanks -- yes, we do think it's lucky!" but if they kept going I'd be backing away because it was weird how people had such strong feelings about my kid's hair color. Some people are weirdly intense about red hair.
I had red hair when I was younger and experienced this too, but honestly, it's more a one off. People who know you aren't talking about your hair all the time. It becomes something older people always comment on at a wedding, but that's not that big of a deal to field every now and again.
I hope DD isn't made fun of in school due to her hair. I've heard that can happen sometimes but did not experience it growing up. Her hair is a brighter red than mine was, though.