4 Do not answer a fool according to his folly,This, in essence, is the perfect answer to the question, "Should you debate an intellectually dishonest opponent?"
or you will be like him yourself.
5 Answer a fool according to his folly,
or he will be wise in his own eyes.
Yes and no.
Yes, because you have the chance to demolish the fallacies and point reasonable listeners toward the truth. And if you don't, someone less qualified (or capable) will try--and if they fail, they'll only make things worse.
No, because you'll fail anyway, not only because your opponent will use every trick in the book to "win" the debate (and your audience may not be able to tell the difference between a "win" and a win), but their mere presence on the stage will feed their PR efforts.
Of course, if you refuse to debate them, they'll accuse you of intellectual cowardice. Or you may come across as a bully. (Although that's subjective; I think Barney Frank is entirely appropriate dressing down a disingenuous opponent, but perhaps it's because I admire curmudgeons.)
So we're back to the paradoxical advice. Or, to paraphrase Yoda: Do, or do not. There is no win.