The part you haven't come to yet is the Harm Principle.
Yes, Mill's general principles for liberty exclude the right to harm others. But he's very very skeptical of considering speech a harm. He's not a counterexample to the literal sense of what you wrote upthread about "saying whatever we'd like without fearing repercussions": e.g. you should be legally liable for libel, and socially liable to individual opprobrium. But he was clearly against the kind of repercussions for the kind of speech we're talking about here.
Okay. So if we're preventing harm, then, what is the possible harm here? Do you think intolerant beliefs threaten society? I'm of the opinion that beliefs mean nothing until acted upon, that only intolerant actions threaten society.
Or to rephrase it as one of the core tenets of Silicon Valley, "Having a great idea is not enough. It is the manner in which ideas are executed that counts."[1]
1: https://news.ycombinator.com/item?id=2318849, linking to https://archive.is/U6C4l#selection-2043.104-2043.196
> But I deny the right of the people to exercise such coercion, either by themselves or by their government. The power itself is illegitimate. The best government has no more title to it than the worst. It is as noxious, or more noxious, when exerted in accordance with public opinion, than when in or opposition to it. If all mankind minus one, were of one opinion, and only one person were of the contrary opinion, mankind would be no more justified in silencing that one person, than he, if he had the power, would be justified in silencing mankind.
> [some pages later:] For a long time past, the chief mischief of the legal penalties is that they strengthen the social stigma. It is that stigma which is really effective, and so effective is it that the profession of opinions which are under the ban of society is much less common in England, than is, in many other countries, the avowal of those which incur risk of judicial punishment.
My understanding of Mill is quite against this claim, and especially your claim upthread 'There is no work of political philosophy anywhere that suggests we should be able to say whatever we'd like "without fear of repercussions".' He was arguing directly this idea that it's enough for free speech that the state not suppress it.