If biracial relationships aren't worth trying, then half-and-halves like me would cease to exist. Total brown dude here. Greek mom and Black dad.
My mom told me stories about even at a relatively socially accepting military base, that she could encounter people in the neighboring outskirts that had grief with a white mom trotting her brown child around. Even my mom's best friend (and how quickly that ended!) gave her grief. If anything, it cemented a really simple idea: if you love somebody and accept them as they are, then skin color, culture, background, these things are no the litmus testing.
I think if you care for someone, then the public opinion of others shouldn't matter. You just go with what feels good.
I am thankful. I have only had one girlfriend for whom my race was a problem, and looking back, the hills of Kentucky wouldn't surprise me one jot. The idea that parents would "disown" a kid over skin color. I remember stating rather plainly, "Hey, funny how you didn't have a problem with me even after hearing me speak" since I don't sound hood, "until she compared me to Martin Lawrence." I hung up the phone.
I'm not gonna lie. The only race-dating issue that bothers me is hearing justifications for people saying things like "I'm not into black guys," "I'm not into Asians," etc., then insist that they are not discriminating. Even after reading Hope in a Jar and getting familiarized with the ubiquity of white skin in modeling and the beauty standard, that's just one set of mental acrobatics I can't get around.