This "paradox" is resolved by https://en.wikipedia.org/wiki/Streitbare_Demokratie - self-defending democracy. Before this idea, a democracy would allow itself to be subverted by allowing a dictator to be democratically elected, and consequences be damned. Not a good idea as we find out.

By extension, a system that wants the idea of free speech to stay viable needs to protect itself from ideas that bring harm to it. Maybe it can be argued that from mathematical sense there is some kind of paradox (a set of all sets that are not blah blah), but this is no contradiction for us humans. There is no mathematical beauty in submitting to a wave of harmful, malicious misinformation.