For a better example of a case where rational debate is useless, I'd take an exiled Tibetan and a Chinese Nationalist debating about the status of Tibet.
I think that's somewhat more amenable to rationality - the "Screw Tibet, free China!" bumper sticker I once saw comes to mind here. But I mostly picked abortion because it's the most prominent such example and the one I've thought most about, not because it's necessarily the best illustration.
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.