Part of me thinks that such a close friend would have shared some of their inner hate at some point, and I would question one's reaction to it. Do you denounce these beliefs to them? Does this person accept you denouncing them? Or do you turn a blind I to this extreme form of hate filled discrimination, and let this distorted way of thinking live on?
I would not judge you for your affiliations, though I do have my doubts about the label being a "close friend", as I am very outspoken to these forms of hate, and one who believed in that sort of cultish ignorance would certainly not consider me a friend.
On the other hand, I have nothing to lose, and I am in no danger of letting the exposure of discrimination spoil myself, or my convictions. So I would be hesitant to let this person build up justification for hate, by making myself come across as the one filled with hate and self righteousness by alienating them. I would actively try to change this person's mind, because removing a positive presence from this person's life might do more harm for them, than good for you. You have sway, and I would hope that you could stand up for history, and the future of prosperity, by being an active influence in changing this persons mind.
As for ignoring the elephant in the room, or being civil... well, I could not ignore the conversation. We stand on the shoulders of those who have died fighting for equality, and to let discrimination live, especially in the hearts of those we love, would be a horrific way to affect change. Even family wouldn't be a tall enough barrier for me to accept prejudice and bigotry, and I would hope that you can be strong enough to make the right decision.