Generally, an independent judiciary is the arbitrator of truth.
Free speech has never been absolute. Free speech does not protect intentionally false speech. For example, tricking people to give you money is fraud. Libel is too. You can support free speech while also protecting truth. When the issue pops up, a judge determines who's right and wrong.
Almost all of the content the Authoritarian left wants to be banned today the independent judiciary has already ruled many times to be Legal Speech under the US definition of Free Speech