I remember something you said: "the Republican Party is the party of people who prefer feelings and aesthetics to facts."
I once got into an argument with a rightist on here arguing that UK race riots are proof that Britain is plagued by Islamic crime, to which I responded with a graph from the Office for National Statistics showing that crime in the UK peaked in the mid-90s and has been on the decline ever since, and pointed out that, by that standard, George Floyd protests prove that the US police is institutionally racist. His response? Assert without any evidence that left-wing UK governments are doctoring statistics to hide the failure of left-wing politics and that the BLM riots were a left-wing plot.
Feelings and aesthetics over facts indeed. How do you even reason with someone like that?
I mean, the short answer is that you don't. They're not making an argument based on reason, so you'll never be able to reason them out of it.
The slightly longer answer is that you can still continue to debate, as long as you're clear that your target audience is not the person you're debating with.
This is an important question, though, so I think it's worth answering in full. Here goes.
So the question of debating someone who's clearly in conspiracy territory has two parts, how much time do you have and what do you expect to gain?
Ultimately, conspiracy theories aren't about reason or logic, those things come later and are, ultimately, just pretextual. If you knock them down, they'll just find new "reasons" or, if it's a long enough delay, just start using the discredited ones again because they're not the important part of what they're trying to say.
I literally cannot recommend The Daily Show podcast Jordan Klepper Fingers the Conspiracy enough, it's one of the best deep dives into what conspiracy theories really are and how they form. In particular, you should watch this episode with Dr. Elise Wang who really lays out exactly what a conspiracy theory is to the person who holds it.
To summarize, a conspiracy theory is, at its heart, just a story and, no matter which conspiracy they espouse, the story is the same. It's "Once upon a time we were happy and healthy and prosperous, and then THEY came. Only no one knew that they came because they hid everything and I'm the hero bravely fighting to defeat them."
And, of course, it can't be any ordinary evil, it's always over the top, blood of children type evil because, the more evil your enemy, the more heroic you are.
Once you understand conspiracy theories in that way, you can see that arguing with them using facts and logic isn't going to get you very far. To make any progress, you have to attack the emotional story but, obviously, if you're distant from the person or time limited in your interaction, there's no way to develop the rapport necessary. If that's your goal, you're best off just not engaging both for their sake, denying them the emotional narrative of "fighting", and for the sake of your own mental health which will not long survive the ordeal of beating your head against that particular wall.
But, here's the thing, that doesn't mean that debating is useless, you just have to shift how you approach the debate. Specifically, the "what do you hope to gain?" part.
There are two main types of debates or arguments, those that happen in private, where only the two people involved can see and hear what's going on, and those that happen in public, where others can observe what's happening.
In order to actually change someone's mind (on anything really, not just conspiracy stuff) you have to be talking in private. Changing your mind can be hard and people need a space where they feel safe and time to process in order to do it. Maybe it happens occasionally, but almost no one changes their mind in the course of having a public debate.
Any debate you have in a place that is visible to others, including social media posts, is a public debate and is not a conducive space for a debater to change their mind. If any minds are changed in this setting, it is the minds of the people observing the debate.
With that in mind, you should alter your expectations and, thus, your strategy, accordingly. Facts and figures are good; they won't convince your opponent, but they're the first step in convincing your audience. When your opponent denies their validity, request that they provide evidence. When they claim it's being suppressed, request evidence of that. Whatever they claim, request that evidence be provided, making clear that they don't have any.
The entire time you're doing so, point out that you have provided evidence and also point out exactly what it is they are claiming. Falsifying national crime statistics, for example, isn't something a single bureaucrat at the Home Office can do because the national statistics still have to be coherent with the collection of local statistics. Now you're not just looking at one or two people, but thousands of local officials who all have to be part of the conspiracy, all of whom have to coordinate properly, and all of whom have to keep their mouths shut.
When was the last time a group of more than hundred people kept a secret for more than a week?
Your audience, ultimately, needs to walk away understanding the things: you have provided evidence for your view, they have not, and what they are claiming is so unlikely as to be impossible.
If you have done those three things, you won't have convinced your opponent, but you will have won the debate as much as it is possible to win it.
Now, if you're debating on private over a longer time with someone who you have some sort of personal connection to, that's a different story. Let me know if that's the case and I'll give you some tips that should help with that undertaking.