There is information circling around as well that suggests a number of these participants on both sides, agitators really, are paid actors otherwise known as shills. Some of the inconsistencies arise from the fact a good amount of the actual Nazi regalia seems to be fresh mint and press - many flags with creases from being boxed and their colors not worn. Other indicators are that the Unite the Right rally itself has ties to the Far Left in its organizers who, until just now, had only just aligned themselves with Trump during his campaign; the same people you might remember him disavowing during his run and was played by the media in much the same way they are now (that Trump and his party are all Nazis or sympathizers).
This becomes more worrisome because the Charlottesville rally was a legal demonstration. It had an actual lawful permit to be held; the counter-protest did not and there was no vetting to keep the two extremely hostile sides divided from one another, first seen with the candle and torch rally on the night of the 11th. This escalated as more outsiders from leftist extremist groups like Antifa and Black Lives Matter came in on the next day. Before the demonstration had even started, the police had still yet to seperate them. We all know what happens next as the mayor overrides the permit to assemble, the police funnel in two violent groups and chaos ensues.
What I take away from this now and where we are at in conversation is that the Alt-Right here, those who received that label, are a myriad of opposing forces. In fact, I spoke to this eons ago in this very topic that the "Right" is at war with itself; you can see this in the Republican party actively fighting Trump to the Trump supporters booing, fighting and apprehending Nazi disruption during old rallies he held prior to election and to now where we are, when an event called "Unite the Right" is held to collaborate.
The "Southern Nationalists" are exactly who you would think they would be. They are the traditional angle that people have stereotyped them into with a fresh coat of Alt-Right paint slathered on them by the leftists and the media. The Nazis, who by being Nazis are not technically "Right Wing" other than their tendency for extreme Authoritarianism (which is independent thereof), are one of the few who fall under that actual label in its first uses. It seems guilty by association is very much alive despite them being outcasts from the "Alt-Right".
The "Alt-Right" presented here is an entire spectrum of ideals. You have everything from your Neo-Cons, Libertarians, Traditionalists, Isolationists, Republicans to your extreme fringes like Ancaps. They are only as "Alt-Right" as each individual might be; they are a mess of competing identities.
The Proud Boys and Alt Knights were organized internally to make a display and show up - most of those flying the white and black flag, wielding shields and batons - and act as regulators. As said by others, they are an internet movement come to life that believes in "pro-Western values". By their own accord, they are "Alt-Lite", which is to say quite accurate; they are a very tame organization and have not yet defined themselves given how recent they are (originating in 2016 officially). As a whole, they just seem to be an organized form of the "Alt-Right" with deep roots in online personality.
Then comes the 3%'ers who are a traditionalist, minimalist, Constitutional organization with extensive paramilitary training and doctrine. Interestingly, they were born out of an abandoning of left-wing politics and socialism. The Oath Keepers are not far removed, the two oft working together, who stand for "the defense of the Constitution against all enemies, foreign and domestic". Both of these groups are unrelated to the rest, appearing in just about every rally where conflict is expected. They are not so much "Alt-Right" as they are a modern militia, but as one can imagine, the Far Left is none too fond of their motives and operations.
What does this all mean?
The label here you are seeing applied maybe makes up half of those who are the actual Alt-Right and not the "Alt-Right". The amount of spin bring shoveled on by the media should be the subject of ridicule, mind you they are the same people who blackmailed someone over a video they didn't like. The short of the story is that the local and state government failed horribly, allowed two extremely dangerous groups of people to mingle, let them fight, and then pushed them into a fatal funnel that then killed someone.
Where is there not condemnation for the counter-protesters turning this into a riot? Why is the President of the United States receiving blame for not explicitly condemning "white nationalists" when he exclusively spoke against all forms of violent extremism? Why is the mayor, who I add has Far Left ties, not being put under a thorough review along with his chief of police for failing to control a riot that led to a death and two policemen dying in an accident? Why is it that all of the Trump base, such as The_Donald or even /pol/, unable to find talk about the organization of this on their own sites despite being extremely active in this sort of protest like they were for Berkerley? Why is there a huge amount of paid shills pushing misinformation on the internet about Charlottesville in just about every comment section?
Call this cat mad, but this is absolutely out of lane.
This is more important to note with where we are in conversation. Calling a person a "Nazi" has lost so much impact that the actual Nazis now blend in. What do I mean by this? When you view everyone who holds the ideals of "Our country we care about first!" as fascism, suddenly everyone who isn't a globalist is a fascist nationalist. Now add in that these people are likely to believe "Illegal immigrants most go." to varying shades and that we need a border wall, now suddenly they too are racists. Racists? Fascists? Sounds like Nazism to me.
This becomes even worse in the "echo chambers", to borrow terminology, of very liberal, left leaning schools up to college. Because now you are subject to indoctrination, where this myth is repeated; that some how socialism and communism are ideal and good for everyone, but politely stripped of those nasty details like Hitler's Germany or the Soviet Union, let alone Communist China and the Great Leap Forward. Everyone who opposes this must be Nazis as we established - who wouldn't want free health care? If you do not, you must support the idea of people dying! Free birth control and abortions? Everyone deserves that because they are so expensive. If you are against that, you must be a misogynist.
Very quickly one can witness how this evolves to where we are now. Everyone must be a Nazi if they are against any of these things. The amount of overlap, despite obvious failings in logic, is startling. I say this because at bare minimum, anyone looking from the outside in can tell you that the Right has no semblance of unity in its message or approach (the failed repeal of healthcare is the best current example I have).
In contrast, the "Social Justice Warrior" department are much easier to peg by their competition, despite this term now too having less an effect because the divide is so massive in the two. Odds would suggest that if you are going to call someone that, they likely do hold a number of those beliefs because of that overlap and immersion they are in. The Left as a whole generally agrees on their tenants as it is right now.
Does this make it right, let alone polite to throw labels around? Absolutely not, but we are at that stage of insanity where this is the norm.
