If you think you can win an argument simply by being right, you are wrong. It is not having better facts that determines who wins an argument. The one who wins the argument is the one who controls the frame of conversation.
People who make the most baseless of claims are the people who are least worth engaging, even if you think you can easily counter their points, because they aren't empowered by facts as much as they are by simply being on the attack. Fascists and conspiracy theorists, for example, tend not have very coherent ideologies. They grow into the strategy of attack because little else works for their positions. They will make a claim, you will counter it, and they will just make another claim. Your counter won't matter; they won't even address what you said. All that matters here is that they are on the attack and you are arguing on their terms.
And they won't run out of things to say because their arguments are not held to the high standards that you probably hold your careful responses. Anyone watching without full attention will just see dominance being asserted over you. Even those who know your arguments are better reasoned are going to get a subtle sense that your defences are being worn away, while the other side appears to be actively standing for something.
And the points made, even if they are incorrect, will remain in the memory of those who heard them. If you have complex statistics and logic, this is a lot easier for them to forget than the simple mantra and confident delivery used by your opponent. All they have to do is have to hear the talking point repeated on a couple more occasions and it will start to seem commonly believed enough to true. There's evidence (Frequency and the conference of referential validity) that even people with prior knowledge about a subject are at risk of believing outright lies just from hearing them enough times.
You might even end up defending positions you don't even fully agree with, just because you know that what was said was wrong and you're unable to escape the urge to correct it. You may get a strong urge to point out the truth in all cases, and this urge is actually very self-destructive. It normalises the dishonest narrative frame and distracts from your real beliefs. You will end up looking bad.
The only good engagement with these people is dependent on two conditions. The first conditions is that you do not let them start the argument on their own terms by letting them get you into a defensive position. They are not interested in working out the truth of a matter with you, dialectically, just in rallying support for their beliefs using psychological tricks that they don't even fully understand are in play. Keep in mind that being on attack is the most important thing, and focus on delivering a ruthless critique of your opponent's beliefs instead of a defence of the pure nonsense that they want to accuse you of.
The second condition is that you are punching up. Pick enemies who are more popular than you are and set your sights on dethroning them. If you have a large presence on a platform like Twitter or YouTube, never retweet or reply to a fascist or a conspiracy theorist who is smaller than you are. It will be good publicity for them, no matter how much you think your argument crushes theirs, and the little growth that they recieve can sometimes be the start of something much bigger. If you feel very attacked by them, and really want to set the record straight, you can do this without engaging them at all. Take your proof which counters their claim, or your position which they misunderstood, and present it to your followers/ subscribers/ readers directly. Don't repeat the language used against you any more than is necessary and keep it all as anonymous as possible.