I think bi-racial relationships are very well accepted by most people anymore. However, there are always those who will have an issue with it, but we can say that about anything really; Tattoo's, piercings, wearing all black. I mean there is always going to be someone who thinks they are entitled to an opinion.
This reminds me of a few weeks ago. My sister had called to tell me about something my nephew had done, they are bi-racial. Most of them are half black/white one is Hispanic and then she is raising her fiance's boys (full black, different momma) while he is having a vacation courtesy of the state
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Anyhoo, she was out shopping with most of them, when a man in his 40's approached her and asked if she was babysitting. She was like "No they are mine", he get's this look on his face and goes "Don't you think they are the wrong color?". My nephew, who's around 10/11 goes off on this man, and may have said a few things he shouldn't, I will grant, but my sister was not concerned with what the man said, only with what my nephew said.
I told my sister my nephew was right, maybe not his choice of words, but that that man had no business saying what he said. That she should not have "just accepted" it and moved on. That by accepting it she was letting her kids think that he was right and there was something wrong with her kids. Not to mention how those kids felt hearing someone say that about him.
I wasn't telling her to give the man a beat down LOL, just that she needs to have comebacks for when she runs into that kinda negativity.
So yes, racial bigotry does still exist, but in small pockets. As a whole I think people don't really care, but ignorance is every where.