If it happens, which it does, as far as I can tell the only effective damage control strategy is to abort the conversation.

My ideal approach (not that I always do so) is more to stop taking sides and talk about the plus and minuses of each side. My position on a lot of subjects does boil down to "it's really complicated, but here are some interesting things that can be said on that topic". I don't remember having problems being bombarded with slogans (well - except with a creationist once) since usually my answer is on the lines of "eh, maybe". (this applies particularly to consequentialism and deontology, morality, rationality, and QM).

I also tend to put the emphasis more on figuring out whether there is actually a substantial disagreement, or just different use of terms (for things like "truth" or "reality").