No, the reasonable response is to completely ignore what they say, because otherwise you are still being manipulated by the liar.

It's easy to ignore the liar themselves, but it's impossible to ignore repetitions of the liar's message. The only possibility is to ignore any message matching the liar's, regardless of provenance. This completely screws up rational discourse.

And yes, such manipulation and corruption of debate is the general problem with liars being awarded leadership positions.

So instead of looking at the facts, and then taking others opinion, you completely disregard the facts because the opinion comes from a liar?