This works in 2 levels. If they know their arguments are dishonest, it's important to call them out on it and let them know that their BS didn't work, and that they have further debased themselves in the discourse by attempting a bad-faith argument. We need to dispel the myth that playing dirty and arguing BS has no consequences. It has severe consequences, as the bad-faith actor loses credibility, respect, dignity and their seat at the table.
If they don't know that their arguments are dishonest, calling them out allows an opportunity for progress, by engaging in the discussion to show them how their arguments are BS, and how they've debased themselves, exposing their ignorance, their bad company and sources, and pointing out how they are losing their seat at the table if they don't sharpen up their civics.
Either way, taking the "high road" against dirty politics serves little purpose. Calling them out and holding a mirror to their dirty faces is essential if we are to have real dialog. Bullies only know strength.
The response to a low takedown attempt is a knee to the face, because it says: we saw it coming, you've achieved nothing and impressed nobody, and you are now concussed from the weight of your own ineffective maneuver.
Notice how the "high road" would actually be detrimental because it's enabling. Engaging in discourse with their bad-faith BS only serves to validate their BS, legitimize their argument and show them unearned respect as participants in the discussion. When they act in bad faith, if we don't treat them as bullies deserving of a knee to the face, we've embraced their BS and validated their approach. So, of course, they will do it again and again, and take it further every time. The "high road" people have made our political division worse, not better.
The bully doesn't ponder on their bad string of choices until something shakes them up. If we want our national discourse to regain civility, since we've allowed it to get this bad we now must teach a bunch of people how to behave, by the way of corrective blows in response to each of their BS attacks.
And we must teach the "high road" people to cut it out and smarten up in how they deal with bullies and cultists. You are not going to Kumbaya a cultist away from racism, misogyny and religious adoration for their orange crimelord - because there's no time and space to sit down with each broken, indoctrinated mind and cuddle it back to health. We need to set firm boundaries on how much BS we'll tolerate (and at this point it should be near none), we need to hold a mirror up to their BS to show them how we see them and how much they've lost the argument and the respect, and we need to clarify why they are dead wrong and full of shit, and stress that they are the largely responsible for turning our civics into a mess and we demand that they cut it out.
In a way, America is great because anyone can be president, from constitutional scholars to abject morons and scummy grifters. The land of freedom and opportunity for all. Between supporting Bush and Trump, the GOP has taught us so much about tolerance and inclusion of all kinds of people, not only those that are intelligent, qualified and well-meaning.