That somebody genuinely disagrees with Chomsky's linguistic theories on their own merit doesn't mean that other people don't want to prove his linguistic theories wrong because they disagree with his politics. Both sorts of people can exist.
George Lakoff is one of his fiercest critics and I have a really hard time believing that he is motivated by Chomsky's political views; Lakoff is involved with various progressive and socialist think tanks himself. I'm not sure about (e.g.) Postal, Ross, or McCawley but I've never heard anything about their political animosity to Chomsky either.
If one wanted to go after Chomsky's political views, falsifying Universal Grammar (whatever that means) seems like an oddly difficult and indirect way to do so. Do you really think that someone decided that a deep dive into recursive structures in Pirahã is the way to push for TPPA? I'm totally willing to believe that more conservative linguists might get a tiny bit more of a thrill out of needling him, but again, this seems really unlikely to be a driving force.
If there's any political force that drives people to go after Chomsky, it's the one driving the academic job market. He is A Big Name, and conclusively debunking his theories would set the debunker's career on the fast track. In fact, even a high profile debate with him, assuming it wasn't a complete rout, would probably benefit most careers.
