I put a great emphasis many times on trying to convince people who aren't already on my side. I like to come up with arguments, analyze approaches, that I think will be maximally effective in getting through to people who are on the fence, or who are even (soft) opponents of the position I'm advancing.
At the same time, I recognize that some people just are not open to any kind of meaningful dialogue - and I'm not just referring to the Cultist of Gnu here. Some people don't ever hit the 'converse' stage and are instead, right from the start, in 'attack' mode. There's no goddamn progress to be had with people like that, at least on the issue in question. So why try? At that point I either bail, or I stick around and mock. Latter one's probably a bad idea in some cases - why alienate people who I may be able to talk with, even agree with, on other topics? In other cases - I'm talking about the left-wing diehard atheist - it doesn't really matter. They don't need conversation, they need a Saul on the road to Damascus experience, and I don't have that up my sleeve.
That said... when it comes to certain issues - social issues in general - I don't think intellectual arguments are really the way to go many times, even with people who are open-minded. At least, not direct ones. I think natural law arguments and various other assorted examples of reasoning are powerful in a logical and intellectual sense, but man, they require a lot of investment just to get some people to understand. Great for someone who likes to spend a lot of time thinking about these things. Few people do.
So here's the puzzle: when your opponents primarily rely on - and succeed with - largely emotional manipulation, caricatures and worse, how do you respond while still maintaining intellectual honesty? I think there's ways to do it, but it requires finesse.