The most insidious thing about bigotry is that it doesn't have to be rooted in hatred. Bigotry likes to hide behind the notion that it can't be bigotry if there's no hatred. But all that is necessary for bigotry is prejudice, and a belief that the prejudice is justified.
Sadly, even people who are victims of prejudice, can still themselves hold prejudiced views of others, under the guise of "but that's different".
While not much can usually be done about bigots (cos they don't think they're wrong - to them, it's not a "prejudice", its a "fact") things can be done to support the targets of bigotry. You don't have to engage the bigot at all, but simply be a kind voice to the person being targeted, so they can see that not everyone shares the same opinion as the bigot. Often times, enough kind voices can drown out the vitriol, without engaging the bigot whatsoever.