It's worth asking whether your interlocutors were physical anti-realists or moral anti-realists who got quite confused about the scope of their anti-realist position.
That's possible, but I got the feeling that they wouldn't know what those positions are. Their positions were so self-contradictory that it makes me think that they had simply absorbed some of the zeitgeist without any kind of formal study and then failed to propagate the change all the way across their belief networks.
I wrote the following on my blog last night. I thought that I'd run it past an intelligent audience. Note that what I have referred to as an idea is what we here at lesswrong would call a 'belief'. I changed the name to remove any strange foggy baggage that might appear in the heads of potential readers who are not familier with belief vs belief-in-belief and other concepts like that.
What are your thoughts?