This is a pedantic semantic post. But words mean things, and this is a case where in particular it is important not to confuse and equate two very different versions of the extreme.
It has become increasingly common to refer to crazy, xenophobic, homophobic, authoritarian, market-fundamentalist right-wing assholes as "radical." Nothing could be further from the truth.
For what does radical mean? At its core, radical politics has always been about a fundamental change in the basic assumptions underlying society and its functioning. Anarchists looking to demolish both capitalism and the state were radicals. Communists, looking to demolish capitalism by seizing the state were radicals. Even liberals and social democrats, in calling for fundamental changes to certain parts of the functioning of capitalism and government, could bleed into radicalism if given a push.
But there is nothing about right-wing objectives (of either the blatant fascist state-authoritarian or the closeted libertarian capital-authoritarian varieties) that challenges the current system. Rather, right-wing assholes want to magnify the basic assumptions of our presently-broken society. Don't challenge racism -- expand it! Don't temper capitalism -- strenghtn it! Don't liberate the gays from homophobia -- destroy them! Don't reduce imperialistic militarism -- send it to more places!
There are two general poles in politics, the democratic left and the authoritarian right. Nobody could claim that even the most radical leftist wants to invent a new society out of whole cloth. But the radical left really is radical, "striking at the root" of the problems of society, as the word originally meant. The "radical" right is deeply conservative and reactionary, built around change only insofar as it is more of the same. The left wants a change in quality, not quantity.