David's mom watches his niece and nephew during the workday, and his 4 year old nephew has already been brought to tears several times by Grandma telling him he's not allowed to talk to his black best friend.
I wrote about my Mom being not racist in a family of racists and raising me the same (and us both speaking out) in another comment and almost added this story but it felt a little OT. But it is pertinent here. You're right that the issue is the kid's parents not telling him the truth about his grandparents.
My Mom's parents were super racist and bigoted against other groups as well (Jewish people, gay folks, you name it) and my best friends in Kindergarten were African American and Japanese (2 girls). I was watched by them and they wouldn't let my friends in the house so I actually asked my Mom if I could stop going and go over to my Japanese friend's house (her parents invited me) daily for awhile, and I did! My Nana asked me why I never wanted to come over anymore and I said (allegedly; this story has been re-told by Mom), "Because you were mean to my friends just because they were different colors. I know that's not right. It makes me sad to be around you."
I literally never heard my grandfather say another racist thing (he heard my answer too, was in the room) and neither did my Mom. When he was dying, he overtly apologized for being rude to my friends a few years ago (I was 9 when he died) and said he felt badly for how he lived so much of his life.
Anyway, old people can change. It's just hard to make it happen and hard to say who or what will. My Nana was still super racist. Their kids were still a bit racist (except my Mom). So it's not like I was the miracle kid.
But my point is, it's not going to make your kids racist to be around them as long as your kids have you. Granted, it might take standing up to them when they say cruel, racist things if a kid is in the mix (something to discuss with your SO) so as not to confuse the kid. I knew at a very young age that my grandparents were racist but my mother and I were not. It didn't fuck me up. It sounds like the issue with your SO's nephew is that his parents aren't really teaching him strong values or dealing with the issue of his racist grandparents, so it's confusing.