I think it's worthy of a conversation at least, but premature to say cut off contact with your family if they are neither engaged or living together.
In my mind, it matters which family members are saying this, it is very different if it's his parents who he is likely to see more often and likely raised him than if it's a more distant relative. If it's his parents it would raise a bigger red flag to me.
The comment about how an uncle referred to politicians suggests that there are two separate issue here, one is the racist comments and one is differing political views. I think it is very reasonable to take offense at the racist comments, on the other hand differing political views can be expressed in a more reasonable manner.
It is interesting to me that she says he is non apologetic not for the racist comments, but that, "I shouldn't judge them for, amongst other things, referring to our president in a manner that you wouldn't even publish." In this case, it really matters what that manner is. A racist slur, time to apologize. Highly, and likely rudely critical of his intelligence etc, not necessarily something needing an apology, just a differing view. Rather like saying I won't apologize for preferring either Fox over CNN or vice versa and stating my opinion of the commentators intelligence etc, even though you might prefer the opposite.
They key still will come down to having a discussion with him around how they see their future. If, in her mind, it's either her or them, then she may as well state the up front, so they can all make a decision and move on, there is no point in postponing the inevitable.