For four glorious years I've been using the term idiot hunting to describe the tactic in discourse where people seek out the very worst arguments of their intellectual opponents and present them as typical arguments of that group. I came up with the term for it myself, although Urban Dictionary shows others had already been using the same term to describe pretty much the same thing before I ever thought of it.
But since then I have learned of another term, Kevin Drum's Law, which has a lot of overlap, although it is more Internet-focused. In Drum's own words:
If the best evidence of wackjobism you can find is a few anonymous nutballs commenting on a blog, then the particular brand of wackjobism you're complaining about must not be very widespread after all.
For examples that are both idiot hunting and Kevin Drum's Law, see Twitter users who thought a Japanese earthquake was payback for Pearl Harbor, far-left blogger PZ Myers say a few stupid blog comments tell us all we need to know about a certain online community and Twitter users who were upset that people were concluding the Royal baby was a boy because it turned out to be a boy.
In all cases, we learned nothing about what typical members of specific groups actually believe, and instead reminded ourselves that yes indeed, sometimes people say stupid things online.
There's also another term I've seen, but unlike "Kevin Drum's Law" I don't think it has much staying power. That is the Weak Man argument, a cousin of the straw man argument. It sounds eerily like Idiot hunting, although one is a verb and the other is a noun, in that it selects actual examples of real arguments, but unjustly presents them as typical.
I honestly think "weak man" lacks the pizazz that "straw man" and "idiot hunting" have going for them. It is just two common words that blend easily into sentences.
But then again, I'm clearly biased towards "idiot hunting."