Right-wing, at least in the context of American politics, might be anti-government, but I see anarchists as more left-wing.
The left wing is more authoritarian than the right, at least in a historical sense; thus, the right wing is close to anarchism. The Founding Fathers were probably considered close to anarchists in their day because their ideal government was only one step ahead of anarchy (i.e. as little government as humanly possible).
I'd actually expect someone to say that historically, the Left was more Libertarian than the Right.
Look at what Mussolini and Hitler did during their primes. Their major support bases were labor unions. They enacted universal health-care, fought for higher wages, and encouraged profit sharing among large corporations (i.e. "spreading the wealth around"). Also, Hitler was a strong proponent of animal rights.
Whoa, revisionism! The labor unions were Hitler's staunchest enemies (except the genuine Communists). Not sure on Mussolini; Italian politics are so bizarre and fragmented that he probably had some on his side. But certainly labor was as anti-fascist as you could be in the 1920s and 30s.
Mussolini's blackshirts forcibly disrupted labor meetings and beat the s**t out of socialist organizers. He was no friend of labor.