Yes, we really can't have it both ways. Either we have free speech for everyone, or we have censorship. There are exceptions, of course: calls to violence, libel against non-public people, and so on. And yes, also inciting panic by crying "fire" falsely in public places. But I believe that's distinguishable from spreading "fake news".
The problem with censorship is needing to trust censors. And even if we have honest censors, how do we know what the "truth" is? Do we trust "authorities"? That seems iffy, given how often we've learned that they've been dishonest or just plain wrong.
Also, authoritarians always start with the edge cases. And then they widen the scope. By the time your position -- which always seemed so reasonable -- becomes unacceptable, it's too late.