First of all, the Nazis actually managed to pull that trick before.They convinced enough people to vote for them to get into parliament, then leveraged politicians who underestimated Hitler, defects in the German constitution and apathy to take power.
I would argue that it wasn't something that could be prevented by muzzling them (if anything, I suspect it would have made them even more popular). Generally speaking, if your society is so close to the brink that it can be pushed over by an election, it's already well and truly fucked. The real fix is to not get there in the first place. In a healthy society, a Nazi-like party would gather some protest votes and such, but would never be in a position to define policy.
For instance, in a first past the post system (like the U.S.) third parties have virtually no chance to gain any influence at all. That means that many political viewpoints are ignored, and power remains with the entrenched parties, which are not required to act in a democratic manner (superdelegates).
This is not entirely true. In the American system, FPTP merely pushed a large chunk of political squabbles inside the parties, with primaries instead of general elections. And extremists can still gain political power that way - just look at Tea Party. For all the ridicule heaped on them, they did sweep quite a few states, enough for a strong faction of their own in the parliament. Again, this is an indication of an ill society, and not something that you can resolve by legislation - at best, you can sweep symptoms under the rug for a while.
If you really think that no form of speech is worth restricting, go look at how ISIS is recruiting people. That's pure speech.
I'm fine with restricting speech that directly leads to a crime. This is basically the "imminent lawless action" standard that is currently in force in US. The key part here is "imminent", and the onus is on the prosecution to prove such. It gives you the ability to prosecute people who actually manage to incite someone to a crime (because in that case the commitment of the crime is prima facie evidence of imminence), and it also gives some wiggle room for cases that are very borderline, but it's hard to abuse because it's so strict.
In case of ISIS speech, it boils down to this. People should be allowed to advocate for it, praise the virtues of the Caliphate, argue in favor of Sharia (including the promotion of death penalty and torture killing for apostasy and adultery) etc. That's all free speech. When it becomes a specific call to action that is illegal (e.g. an invitation to join ISIS), and that call is not just a random diatribe but is actually directed towards an audience that is likely to heed it, then that becomes fair game. And, of course, giving specific directions on where to go and whom to talk to in order to join, or providing specific instructions on how to wire money, is fair game.