I think it all depends on the context in which it is being mentioned. If we take two strangers waiting in line at a grocery store, both of different backgrounds, we can start to paint a picture. How would you start a conversation with the woman in front of you? Let's say she is black, what would you say? Surely something about her ethnic appearance isn't going to be one of the first things that come to mind, ask yourself why and I'm sure you have your own sufficient answer.
Tell her that you like her hair. It's different from your own, but it's a genuine compliment, you may not know how she got it to stay like that, but it's admirable. Instead of saying, "how do you get your hair to stay like that?" Why not ask, where do you go to get your hair done? Or, what products do you use? Etc. There are better ways to acknowledge race without being an ignorant or insensitive jerk.
I think the biggest problem is lack of empathy and effort to even try from all sides, but that's my opinion.