Freedom of speech doesn't aim to protect speech that is 'nice'.
"Like other tyrannies, the tyranny of the majority was at first, and is still vulgarly, held in dread, chiefly as operating through the acts of the public authorities. But reflecting persons perceived that when society is itself the tyrant - society collectively, over the separate individuals who compose it - its means of tyrannising are not restricted to the acts which it may do by the hands of its political functionaries. Society can and does execute its own mandates: and if it issues wrong mandates instead of right, or any mandates at all in things with which it ought not to meddle, it practises a social tyranny more formidable than many kinds of political oppression, since, though not usually upheld by such extreme penalties, it leaves fewer means of escape, penetrating much more deeply into the details of life, and enslaving the soul itself. Protection, therefore, against the tyranny of the magistrate is not enough: there needs protection also against the tyranny of the prevailing opinion and feeling; against the tendency of society to impose, by other means than civil penalties, its own ideas and practices as rules of conduct on those who dissent from them; to fetter the development, and, if possible, prevent the formation, of any individuality not in harmony with its ways, and compel all characters to fashion themselves upon the model of its own."This book may have been pivotal to British utilitarianists, but it didn't have much, if any, impact on the U.S.
Before then, "free speech" as a concept did not exist. (The closest was the freedom of religious practice, which is not the same thing.)
Now that is a heavy claim to be making. Do you have anything to back it up?
Before the U.S., nobody even thought free speech was possible. England was the closest, but their version of free speech was still subject to government censorship.
It was the writings of the Founding Fathers, and the Bill of Rights in particular, that established the doctrine that is today known as "freedom of speech."
"The free communication of thoughts and of opinions is one of the most precious rights of man: any citizen thus may speak, write, print freely, except to respond to the abuse of this liberty, in the cases determined by the law."
Specifically, how does banning people for their actions work well as an analogy for banning someone for who they are (and you must take that for granted, because that's the legal frameworks opinions on the matter)?
That's also an even worse example because the supreme court found in favor of the cake shop.
I think this analogy needs a lot of work.