And the liberal answer to that is not "so shut the morons up so they can't spread lies to each other". That's the authoritarian answer. The liberal answer is "give everyone a great education, so they no longer have such limited understanding".

You've taken the easy path here and dismissed Mill's arguments by assertion. "Clearly mistaken" you say, oddly ignoring 250 odd years of history where it seemed to be working more or less like he said, and apparently attending only to the regressions of the past decade or so. With your limited understanding, you are regressing to antiquated beliefs about having to control what people say. We need to stop giving a platform to your intolerant ideas of making people shut up when your opinions differ from theirs.

Or, just maybe, we don't. Maybe we need people to challenge you (using speech) to face Mill's arguments head on. Here's a starter: https://www.thefire.org/news/blogs/eternally-radical-idea/mills-invincible-trident-argument-every-fan-or-opponent-free

Maybe we need people to call you on the use of "they will not stop until they have abolished all the basic human rights we’ve fought for over the last 200 years" as an argument, because while there are a few people who actually would, there are vastly more who wouldn't, and their speech is not, by and large, compelling. As Popper says, "as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be most unwise".

You have failed to make the case that the breadth and strength of intolerance is the kind of existential threat to tolerance that would even evoke the Paradox of Tolerance. (And even then you'd have to argue that you shouldn't take a Rawlsian view of self-preservation which appears to be slightly weaker than Poppers, but still preserves tolerance.)