An illegitimate side according you, might not be illegitimate in general.
I'm not saying there are no universally illegitimate sides, but even those have their supporters and some reasonable arguments. The focus should be on deconstructing these arguments instead of marking the side as illegitimate.
The way I see it, we're drawing from a pool where most ideas are bad. Most problems (or, more broadly, "systems") have unsettlingly narrow parameters under which we can secure a beneficial outcome. Like the human body: a very narrow happy path flanked on both sides by a boundless abyss of deranged and dysfunctional pathologies limited only by your imagination.
I don't have an answer for how to identify good ideas that's convincing to everyone, especially in the flimsy-whimsy domain of politics, but I believe there are always more than two sides even if it's presented that way. There are uncountable many "sides" and most of them are bad, wrong, and insane. And to entertain all of them in earnest under the pretenses that we're being fair is a paralyzing waste of time.
Even for a comedy show. It's not really about the show anyway but the bigger picture of politics that it fits into.
Oh there are you know. Some people want to murder other people that they have never met and don't know, also they want to murder those people's children. These people don't have some reasonable arguments, instead they have a shared assumption of hate and (im)moral purpose.
I have to say, I don;'t see this as a counter - isn't it a norm and a good idea to try and avoid wars and stop them as quickly as possible? The implacable hatred of "the other" is the problem - not the reluctance of the sane to debate with the folks who have the implacable hatred issue.
>I wonder what arguments you may see here and what the possible deconstruction may look like.
Consider a debate about the existence of God. A theist person might say 'everything must have a creator'. One deconstruction could be that the proposed God does not seem to have a creator.
I'm not saying there are no universally illegitimate sides, but even those have their supporters and some reasonable arguments. The focus should be on deconstructing these arguments instead of marking the side as illegitimate.