I think he started out as one of the authors whose political writings were influential among the 1968 generation, or perhaps a bit later. It's just that unlike many other influential authors from that period, he stayed alive, and kept churning out political writings, for a long, long time.
Fun fact: Justin B. Rye, who's politically very far to the Left, but also very much interested in Linguistics, once expressed his opinion that "Chomsky should stick to politics".
I don't see the point of arguing about his precise ideology. It's clearly more a matter of psychology than political theory for him. Like all too many people who are into politics, he mainly cares about going on hating the people he's always hated.
