You probably already knew the answer before you asked the question, but just wanted confirmation of your fears. As much as tv or idealist or p. See. Folks like to say otherwise, yes race is still an issue.
You have to understand, it's very hard for a society (or people) to admit it still has demons and face it's warts. But they are there :D
I am puerto rican, but I live in the south. My features are cuban, but to people think I am half black and half mexican :) I have experienced just about everything you have. But I have had white girlfriends and have really noticed the difference. Black girls would give her mean looks and throw ice at her. When I dated a (I would say) very attractive white girl, older white men HATED it. I would joke about it with her and we would laugh at the narrow minded people and it never phased us.
If a black person is exceptional they have better chances ( as well as a strong personality of the other race, who can disagree with their parents or what society thinks and not let it bother them. This is the minority,btw). But you may still encounter "My parents would kill me if I dated a black guy! " or "You can be my christian brother in church, just don't date my daughter"
We are only 50 years from when black people couldn't vote and were segregated. When you see old film footage of white teenagers holding up Keep Niggers Out signs, those were real people who are somebody's grandparents (only one or two generations removed) you have to know that that generation still influences their kids and grandchildren.
Truth be told it is a lot better than it ever was. In the past you were black you were bad, (second class citizen and rights) you were white you were good ( the best rights) now, if you are black you are more likely to be bad (he might not tip, if he is wearing hip hop clothes he might be a criminal, probably has an attitude or is lazy etc. )and if you are white you are more likely to be good (he probably has better manners and is better educated, he's not lazy he's just laid back etc. )
A lot of it sometimes is not racism, but comfort. Two white people from the same background can relate to each other better and are more familiar than a black person's experience. A lot of people really have never been in that person's shoes, and might not really be able to understand where your perspective is or relate to your reality and experience
Not everyone is like that, especially now, this generation is the least racist it's ever been. Which is great, I am very proud of how far we have come. But believe, that we still have a long way to go. It's okay though, this is human nature. (look up other historical cultures that always have had a need to separate themselves as superior to people EXACTLY like them)
Just date girls that treat you the best, whatever race that may be.