It is stupid especially considering that the people who are for this sort of censorship (or moderation, if you will) usually also agree with the notion that we are heading towards fascism. Which one is it then? Is it possible to take on step forward and stay put, or does every step forward indicate more steps in the future?

You can't have it both ways, it's either a fallacy or not. History tells us that it is not a fallacy, and that we should use all the warning signs we can find before it's too late to go back.