Well, I haven't been so forgiving with my extended family about this. In the end, my kids were not influenced at all, because we discussed all the terrible stuff they heard and they ultimately ended up rolling their eyes, too.
DH's parents were terribly racist, but not in an overt way. It would slip out, though. My maternal grandparents and my aunt and cousins who live locally, are some of the most xenophobic people I know. Holiday dinners when my kids were growing up were always political fights. Heck, I have my grandfather on video, talking about back in the day, when "Rose Kennedy was (insert Yiddish word for having sex) with all of the Jewish boys." Yes, this was the tone of my family. It was so awful, it was funny. These people are/were afraid of anyone who is different. For example, for quite a few years, they rented a house on the Cape, where another family who sat near them on the beach had a multiply handicapped daughter. They went on and on about this girl. It was like they were repelled but fascinated. Another time, when my oldest cousin was about 12, he went to visit my parents in AZ. They were in the grocery store and a guy with a gun hanging in a holster walked by (needless to say, you don't see this in MA). Apparently, my cousin had such an anxiety attack when seeing this "cowboy," my mom had to bring him out of the store and go home. And if a person of color ever ended up in their neighborhood, they talked on and on about it.
I guess what I did worked, because my my youngest son first joined the Marines, he told me he had more in common with the kids who grew up in the ghetto than the "rednecks" from small towns who just had no life experience with different types of people.