Well, it would depend on the situation.
My granddad will make racial slurs because it was acceptable in his day and he doesn’t care enough to correct it. I don’t like it, I tell him to stop being vile, but I wouldn’t disown him for having an outdated vocabulary and mindset. By racial slurs, I mean things like “that young paki girl friend of yours, what’s her name?” Not intended to offend, just outdated.
My DP is black. If a family member was calling him derogatory names and being racially abusive to him, then I would probably distance myself from them.
I have family members (uncles and cousins) who have pretty awful views on anybody not white British. They haven’t met DP so it’s never been aimed at him. But in general their views offend me. I don’t disown them but I let them know I don’t agree with their views. They’re very uneducated. You can’t reason with stupid sometimes.
So I guess in short, I would cut off somebody whose views impacted on me (DP) personally, but would just distance myself if I wasn’t personally impacted and they just had poor views.