MissAdventure, I always used to describe my children as mixed race and none of us felt bad about it. I think it has gone out of fashion now. I know some people say "dual heritage", which I think is quite nice and tend to use in writing. I just feel a bit pretentious when saying it.
Regarding the OP's dilemma, I think it is hard to feel the same about people when you know they are racist. It just changes the way you feel about them. It also means that you are on edge in case they say something offensive, and you're willing them not to. Either you compromise your principles or you have a big row. Not good, either way.
It's more complicated when it is people you love. My grandmother was a sweet old lady but an outright racist. My sister and I used to have fierce arguments with her, which achieved nothing but hurt all round. She was born in the Victorian age and nothing would change her attitude. I loved her but I hated her prejudice. My mum's sister, my beloved aunt, was also very prejudiced. I loved her too and couldn't understand how such a kind person was such a bigot. We thought that she would react very badly to the news that my boyfriend was Indian. We braced ourselves for arguments but she adored him!
She rationalised these conflicting opinions by saying he was "a cut about the average." The truth was that he was the only non-white person she really got to know.
Confronting racism is very stressful. Some people are in your life for good and all you can do is debate with them. Some you can live without - in that case, ditch them. Do you really want to be mates with someone who believes that some people are inferior by birth?