My grandparents were outwardly racist and prejudiced. It was really tough to be patient when they got going on these topics. In person, I just really tried my best to avoid any topics where these sorts of sentiments might emerge, and if they did anyway, I simply tried to turn the conversation as quickly as possible.
Thankfully, with FB you have more options. You can unfollow them without completely defriending them. If they post this obnoxious stuff on your wall, you can immediately delete it or have a chat with them (heyI love keeping in touch, but i don't feel comfortable discussing race/religion on my fb page). However, if you are the type to get super political/ideological on FB yourself, you need to understand that you are inviting these sorts of situations (so maybe consider keeping your online profile less controversial to begin with). While prejudiced sentiments are obnoxious, only you know if it is worth cutting someone completely out of your life. My grandparents were great influences in my life overall, so it made no sense to just stop talking to them. But if your only interaction with this person tends to be racist tirades, then it might make sense to just slowly stop communicating with them over time.
I personally have had to unfollow a few extended family members due to their fundamentalist religious beliefs that I found insulting/obnoxious. However, they are very respectful when it comes to other peoples' walls/posts, so the unfollow feature was all that was needed.