The difficulty I have is taking an absurd argument and going to the trouble of refuting it point by point, which would seem to validate that the position is reasonable. We see it all the time with the GOP making one crazy statement after another, and then having someone address the argument as if it has merit. I haven't been able to work out to my satisfaction what impact such refutation has on unbiased listeners, assuming there are any such. On one hand, it could be that such patient and determined refutation serves to sway the "undecided" to the side of reason. That's the optimistic outlook, but as I say I'm not so confident that Truth will triumph. The other side of the coin is that the "undecided" are really either not paying attention or are somewhat sympathetic to the crazy argument to begin with. In which case, might not acknowledgement serve to lend credibility?
On the gripping hand, your argument that we ignore them at our peril may just have the most merit of all. I simply am not confident which tactic is best, to attain the goal of shoving these idiots back under the rocks from whence they came. After all, voices have been raised in reason and opposition to a lot of crazy stuff (Benghazi and birth certificates and what-all else), yet in my subjective view the craziness seems to be flourishing. But that could be a perspective illusion, and who can say how much crazier it might be if those voices hadn't been raised? I certainly don't feel competent to judge. And I personally have difficulty suffering fools.
-- Mal