I'll play devil's advocate here, as I am not a Nazi/Nazi-supporter, and am not into these Holocaust-denial fringe theories:

You seem to start with the assumption that these are fringe beliefs that forever stay on the fringe when left unchecked and never, ever have an impact on anyone else. This is simply not so.

You're right, fringe theories are adopted by the population when there is no trust in the "official narrative". If there is trust in a set of beliefs/political system/etc, then people are, by-and-large, too lazy to seek out alternatives. Often, the people who adopt fringe beliefs are the "losers" of society - they would rather adopt a fantastical set of nonsense rather than admit to their own failings.

The suppression of Nazi ideology was absolutely vital to rebuilding the country.

To be unbiased, it was vital to building Germany into its current form; it is highly doubtful that Germany would not have been able to rebuild itself without the suppression of speech, though it would be a vastly different country.

And it's not like there wasn't precedent about just how harmful letting a conspiracy theory run free can be. Are you familiar with the Dolchstoßlegende? It was a right-wing conspiracy theory circulating in Germany after WW1 that said that the German army hadn't truly lost the war but were "stabbed in the back" by cowardly revolutionaries (read: The Jews) at the home front - revolutionaries who went on to found the new democratic Weimar Republic. This conspiracy was widely believed by the German people as it fed into their victim complex and was one of the key tools with which the Weimar goverment's legitimacy was undermined - which allowed the Nazis to take power.

The Weimar Republic took power following the defeat of Germany in WWI via the Treaty of Versailles, which basically made a victim out of the entire populace. It was a case of "shoot the messenger", as the Weimar Government actually did a lot of beneficial things to improve Germany, but were the face of Germany's defeat. This narrative of being "stabbed in the back" was popular among the far right-wing, but was not national sentiment until it was popularized by the Nazi's. While the Nazi's certainly used it to their own ends (thus helping them subvert the Weimar Government), you have the order backwards - "it existed and the Nazi's used it", not "it gave rise to the Nazi's". The Nazi's also utilized the Jews' insular nature, as they preserved a societal identity independent of that of the German Nation (eg. less "Germanization"); you see the same issues with Muslim immigrants in Europe. By your logic, this would also be a dangerous precursor to the Nazi's.

Speech has consequences. And sometimes, those consequences are so much more harmful than the consequences of outlawing it. Your rights end where harm to others begins. I see such unbelievable naivety about this matter from the Freeeeee Speeeeeech advocates.

Speech has consequences. Speech that creates a clear and present danger to another is not protected speech. Negatively generalizing a group who supports a viewpoint contrary to your own is certainly not in-line with the message you are trying to support. Another discussion to hold is, "how is harm defined?" For example, you see a lot of "SJW's" claiming that hearing an opinion contrary to their own is harming them - is this really comparable to harassment? And how should these situations be handled? Through the judicial system, or through a blanket edict meant to suppress a basic human right (per the Universal Declaration of Human Rights)?

Conspiracy theorists are not rational. If they could be swayed by facts and reason, they would not believe shit that even the most minor bit of fact checking would reveal to be untrue. Allowing them to spew their bullshit freely doesn't make them seek out people who'd disabuse them of their notions, it makes them seek out other people who share their beliefs - and who radicalize them further. We see the echo chamber effect right here on reddit.

Conspiracy theorists can be rational (avoiding generalizations), however they lack trust in the established narrative, to the point that irrational behavior is common. Would you believe an unreliable source that claimed the Holocaust never happened? Of course not, because it is so contrary to what you believe to be true that it holds no weight to you. People are similar (no matter what their beliefs) - they will typically not attempt to disprove what they already believe to be true. Legalizing or criminalizing speech will not change what they believe, only how open they are about their beliefs. But you are correct in that they will most likely not change their opinions when confronted with contrary testimony/evidence.

Whether or not the holocaust happened is not a matter of opinion, it is a matter of facts. You're entitled to your own opinion, but you are not entitled to your own facts. Making up your own facts is called lying. And when your lies are so malicious and harmful that they actually pose a threat to other people or the nation itself, then yes, that should absolutely be punishable. It's no different than slander or libel.

First, "facts" are subjective - as they say, "the winning side writes the history books". The narrative is defined based upon whose side of history you ask - take the Nanjing Massacre for example: who can accurate say how many people were killed? Do we follow China's count, or Japan's count, or an "impartial" international count? They're all estimates in good-faith, biased in favor of the country doing the counting. Now on the other hand, there is a difference in disputing numbers to disputing that an event occurred - especially when the Nazi's were as fastidious at keeping records as they were. However, it again plays down into which sources are believed - was the Holocaust the wide-spread, systematic genocide that we all believe, or was it the isolated actions of a few insane Nazi's? Confronting these issues via first-person testimony was incredibly important for this reason.

what's the harm in not allowing holocaust denial, specifically? What is the benefit in allowing it? There is none. Nothing good will ever come out of someone spewing holocaust denial. Ever. You won't get a thoughtful debate beneficial to both parties. They're wrong, simple as that. The "best" outcome you'll get out of it is that you can convince a denier or someone on the fence that they're wrong. Great. The best outcome involves suppressing it.

First, you shouldn't ask a rhetorical question, answer your rhetorical question in support of your point of view, and then immediately provide counter-evidence to your point of view that invalidates your answer. Also, you provide no "best outcome" despite claiming it exists.

Second, this is exactly why speech should be free - you will never be able to fully stamp out an idea without killing all those who hold it. Instead, you use free speech to educate those who are undecided, until the population who supports the 'truth' grows to the point that the fringe has no power. That is the best way of confronting harmful ideas - shine the light of education so that all can see how perverted and diseased the fringe beliefs are. That's how Science did it, that's how America does it... and its worked out pretty well so far. <Joke - you cannot honestly compare the existence of hate/fringe groups in the US to Germany, due to the different laws surrounding free of speech.

The reason that the vast majority of modern Germans look at the Nazi flag and feel nothing but revulsion whereas a sizable portion of US southerners actually fly the confederate flag and defend it ("Heritage, not hate", "It was about states' rights, not slavery", "Slaves weren't treated so bad") is because Germans were forbidden from telling each other comforting lies about their past.

I'm not going to get into this because of time constraints and lack of knowledge, but I feel it would be more accurate to say that the South still supports the Confederate Flag because it represents a time of 'self-determination and power' for an area that currently has a lot of issues with education/poverty compared to the nation's average.

TLDR: I don't disagree with the emotion behind your rant, but it is flawed as an argument.