They came to power by silencing their opponents through force, political posturing, manipulation, and opportunistic behavior.
In fact the Nazis squashed free speech in many ways, and used violence, threats, and coercion to make others silence their friends.
Frankly had free speech been protected and valued by any means. We may not have had a third reich.
Let the fascists speak, let them out theirselves. So that common people can distance themselves.
And unfortunately, once they have power, there is very little that normal people can do to ensure that they will obey by the rules that got them there (i.e. free speech). I would argue that there was no way to prevent the Nazis from squashing free speech except by preventing them from coming to power - and this is true with many malicious actors. Unfortunately, that means we have to balance the need for free speech with the need to prevent malicious groups from coming to power.
Ergo, the Paradox of Tolerance.
This is where the second amendment shines isn't it?
On the other hand, human history has shown that political parties will attempt to censor anything they can. We can see this with the alternative realities constructed by Fox News/MSNBC and we can see it in totalitarian dictatorships like North Korea. I am not aware of any counterexamples of a country where the government does not attempt to influence the narrative.