I have any number of family members that are racist (uh, let me count, pretty much everyone I know) and pretty much all my relatives except my parents and two aunts are varying levels of misogynistic. The most disappointing is my brother-in-law, who should know better but is comfortable in condemning an entire group of people on one really bad encounter (lost a lot of money in business, got cheated out of technology he developed).
I deal with it by ignoring it. Most of the time people seem to manifest it in terms of racist jokes and I find the most effective way of shutting down that line of conversation is to not smile at the joke so it falls with a heavy thud. Sometimes I think particular relatives also do it just for the shock value, so doing the protest/lecture deal just feeds into their shtick.
Half the time I feel family (not immediate, but extended) really try to goad me into a reaction (i.e. dating in general, dating white people, position of Indian women, marriage, having children) by making statements they really don’t believe in or taking positions they don’t care that much about because I used to be really reactionary and fiery when I was young(er). These days I just give a distant “oh really? I’ll give your opinion all the thought it merits” attitude and they give up with apparent disappointment that we’re not going to have some screaming, melodramatic Indian family-drama.