Anne -- I want to challenge you on this a bit. I have found in my own life that race isn't much of an issue. I don't care what color anyone's skin is. But, unfortunately, I am much more comfortable (and thus more welcoming, and more loving in some way) with people who share my socio-economic status -- my education level and middle-class financial background.
I believe this is not entirely healthy, and something that I need to work on. I think it's something our suburban culture encourages. We all live with the same kind of people, which means that we are insulated from other ways of life and other needs. Al Hsu addresses this a bit in his book, Suburban Christian.
I think it might be healthier for me to live in a more diverse area. Or, if I stay in the suburbs, I need to find more ways to reach out and understand others. (Not saying that you don't reach out to others, of course! I just think our suburban environment can make this more challenging, because we have to work to see and understand need.)