The Goblinoid culture is essentially military culture writ large. From the pyromaniacal grunts of the goblins, to the officer corp of the Hobgoblins, to the scary special forces of the Bugbears, Goblinoids are a military, an entire civilization built for conquest. It is almost the exact antithesis of an Anarchist society.
But every military, even one (or perhaps especially one) as all-encompassing as Goblinoid society, has its dissenters, deserters, and drop-outs. With the brutal repression that would face these rebels, their break from mainstream Goblinoid society would be all the more total.
This, ironically, makes these Goblin rebels more likely to adopt Anarchism than many other races. With such a stark rejection of the ideals they had been brought up in, they are less likely to dismiss Anarchism out of hand. Plus, they have seen and experienced tyranny and hierarchy first-hand, in a way few other races do.
Which is not to say that all Goblin rebels, or even Goblin Anarchists, are all good-hearted hippies. Just because someone rejects hierarchy does not mean they automatically gain empathy. Many Goblin Anarchists will be evil, and a good Goblin Anarchist would be about as rare as a good Goblin, period. But the occasional good Goblin Anarchist does exist.
Goblinoid Anarchists tend towards the Pacifist, Collectivist, Insurrectionist, Illegalist, and Platformist traits.