I respect most opinions, no matter what they say, but there are exceptions.
Anyone outwardly racist, sexist, ageist, will incur my annoyance, and while I may argue with them, I won't respect their viewpoint, it's a very different scenario.
I might debate with a religious person (I'm atheistic, mostly), but I will respect their belief, and their right to it. Same with a debate over a book (Twilight springs to mind) I can debate with people, respect their counter-arguments, and put forward my own points, and even if no conclusion is reached, respect has been shown.
Racists etc I will treat with barely concealed contempt most of the time, especially the dogmatic variety who won't even debate, then I ignore them, which from a seasoned debater is about the highest form of insult.