It's a possibility. I don't imagine all of the Firebenders that were staunchly loyal to the Fire Nation getting on well with Aang's N.W.O (New World Order). I'm willing to wager that some of the more socially powerful ones, the ones that had a lot of political clout and a lot of money (a.k.a. a lot to lose), threw in the towel right away; by acquiescing in this way, they would only diminish themselves somewhat with the brunt of it being wounded pride and a lack of autonomy---a better trade-off when considered with the alternatives such as losing everything, being imprisoned, or even executed. They could keep their money and eke out a spot in the new status quo. Others houses and/or other political entities in the Fire Nation were too weak to do anything about it anyway, and going with the sweeping reforms was probably infinitely better than going against it.
Others, however, didn't give up so easily. Whether it was idealism, materialism, or whatever, I can see certain disgruntled individual members of the Fire Nation turning their backs on this **** and doing anything but being under the thumb of this new government. There seems to be a lot of Tong-like cartels operating in places like Republic City; one possible theory is that some of these criminal groups were started by those Firebenders that were once part of the Fire Nation, and they had resources and manpower somewhere that gave them enough wherewithal to start doing things their way. After all, after the death of a Nation, what's a patriot and veteran going to do...? Things aren't going to go back to the way they used to be, and they're sure as hell not going to play by their rules anymore. May as well put that martial training to good use, and use it all for yourself.
There could also be the neo-Nazi sorta Benders that want to restore the Fire Nation empire, as you said. These guys would probably be a super minority after all of these years, but it's very possible that some Joe Blow Firebender's great-great-great-great-great grandson was raised to carry a torch for the glorious days of yore where Firebenders were running the show. It's also very possible that there are more than one of these guys that have this in common. And even still, there could very well be a centenarian Firebender out there that could be spearheading a pocket of these young men. Maybe even more...
Smooth Criminal