Growing up in Oklahoma for the last 14 years as an African-American female, I can say that I've come across a number of perspectives regarding racial sensitivity and tolerance. I've met people who have incredibly progressive attitudes towards the struggles that minorities face and are aware of the privileges that they possess. I have also met people who have unknowingly—and sometimes intentionally—allowed their explicit biases to be reflected in their unwillingness to acknowledge what life is like for anyone other than themselves.
Growing up in a conservative state with a predominately white population, a phrase I've heard time and again over the years in conversations regarding race and ethnicity is "I don't see color, we're all the same". While I can appreciate the nod to equality that's being made here, the clause that makes this statement problematic is the fact that it negates the independent experiences that characterize different groups. Another issue with this expression is the context in which it used, often times it's in response to someone sharing an experience with prejudice or discussing attitudes that are harmful to the perception of the group they belong to. In a situation like this, stating that you don't see the unique traits that make someone unlike you is equivalent to invalidating everything that they've just told because it doesn't pertain to anything that's accessible to you, and therefore is not a big deal. It does not distinguish you as some remarkably progressive thinker that has transcended the binds of conformity and social biases, it makes you sound as though you couldn't be bothered to empathize.
I believe that most people who say this don't do so with the intent to discredit another's feelings, they say this to reassure themselves that if they don't categorize anyone as different from them, then they can't be prejudiced. The comfort that this self-affirmation brings to one is not felt by the person to whom it's being said, what that person hears is "I don't see you".
The heart of the issue with cross-cultural relationships at the moment is the lack of empathy. It's easy to look at the oppression and struggles that one group or individual may face and feel sad for them without any real consideration what it's actually like to go through what they have. It is much harder to look at someone else's experiences from their own eyes, aware of how the rest of society sees that person, and respond with that perspective in mind.
Despite the commonalities that we all share as human beings, when we throw away the things that make us different, we lose even more of what makes us similar. The next time that dropping the line "I don't see color" seems appropriate, stop and think about what's being implied and what you're really trying to say.