I can’t help but think that a central aspect to the problem is absolutism. Not absolute power; I mean absolute truth.
Some simple historical facts, like “WW2 happened”, or “Lincoln was President”, are capable of being determined beyond sensible dispute.
But most of the inputs in arguments are questions like the best balance of government and free enterprise at a level of abstraction that does not admit of absolutism. Discussions about these things require negotiation and compromise.
But proponents in modern debates insist on presenting their side in absolute terms. Their position on Obamacare is expressed in terms that represent their views as having the same truth value as the proposition that the oceans exist. Of course, they don’t.
But if you believe you have the absolute truth, then no compromise or negotiation is possible. Absolute truth is, precisely because of its absolute accuracy, represented as a value that must not be betrayed. It has a quality above all other qualities. Having the absolute truth about the economy or about God, means that there are no limits to protecting it. You can lie, you can undermine human rights, you can kill, all to protect the absolute quality of your truth.
And the same principle is applied in debates. You can shout, be derisory, discourteous and rude, because the possessor of absolute truth is excused from the “normal” rules about such things when absolute truth is on the line.
Of course, as a matter of rhetoric, it suits some to pretend that all the beliefs they hold have this absolute quality. This liberates them from the constraints and restraint of normal discourse and allows (in their mind) any amount of bullying or attention seeking. And loud, simple propositions have always got more attention than nuanced arguments.
Religious absolutists now and historically happily slaughter people in defence of their absolutist views, because of this idea that truth trumps all other qualities.
But naturally, most propositions of sufficient complexity are not capable of being conceived of as absolutely true. They are actually judgments about balance, or guidelines that admit exceptions, or default positions whose applicability may vary in different situations.
So maybe spotting shrieking arguments as attempts to pretend that the debate is about invariant truth might be a step to returning them to the realm of manageability.