Not to mention that "Let's point and laugh at stupid people" is a challenge in and of itself. It's a refusal to view their point of view as anything other than comedy. A refutation of their points actually helps legitimise them.
On the other hand, ad hominem only serves to infuriate them and prevent any sort of useful dialogue.
On one hand, that's true. On the other hand, if you really commit yourself to refuting right-wing nonsense, you're going to be saying the same things over and over again, to people who believe you're a communist to begin with. In the movie, there's a quote "How about global cooling?" - This refers to a popular right-wing meme that during the 70s, the scientists were concerned about global cooling rather than warming. This is demonstrably not true, since the source of the claim are books and a few newspapers covering said books' claims, not actual scientific consensus. When you see that someone's argument, message, or whatever, is full of this kind of stuff, that's when it's tempting, and also justifiable to switch over to mockery - Yeah, we need state-endorsed prayer, along with a statue of Jesus riding a dinosaur, and we should all wear small pins of Ronald Reagan. That kind of stuff is effective if the opponent actually values your opinion, but the problem is that this is the internet, and everyone has to act tough and never acknowledge being wrong and all that.