Most people don't want to live in a society where:
* people can say vile racist/sexist/homophobic things.
* where the state censors what you can say.
But you pretty much have to pick one or the other. The US took the maximalist free speech approach. Europe didn't. Due to differences in culture and history. I think both are defensible on various grounds.
However successive UK governments also seem keen to restrict the right to peaceful protest. I would say that is a different thing and I'm not sure it is helpful to conflate the two.
I don't want people to say vile racist/sexist/homophobic things, but I believe you should have the right to do so anyways (and others should have the right to speak against such things). The government should not censor what you say, even if the result is that people do say bad things sometimes, if you have free speech, then in addition to bad things it also means that people can (and do) say good things sometimes too, so it is good.
It's not a conflation. Being able to protest is part of free speech. It's like saying, the ability to publish a book isn't about "speech" but instead that is actually freedom of the press.
> people can say vile racist/sexist/homophobic things
The definitions of what speech falls under "racist/sexist/homophobic things" tends to be highly subjective and varies between who you ask and who's in power, which means they instantly become hammers of those in power to suppress speech of the opposing camp.
It's basically tools for selective enforcement and will 100% gonna be abused because those in power can never be handed a powerful weapon and expect to never misuse it for personal gains.
Like for example, during Democrat rule, before Elon bought Twitter and before Trump came to power, it was considered homophobic to say there are only two genders, or to even ask how many genders there are, and could get you banned on Twitter and other major platforms. Pointing out crime statistics on illegal migrants was considered racism, and so on.
So once you brush everything you don't like under the "racist/sexist/homophobic" speech, you've successfully achieved totalitarian rule while cosplaying as protecting democracy, which is what Europe is trying to do.
Both of those examples invalidate and/or endanger people though.
For example, repeatedly asking how many genders there are ignores the obvious 'its a continuum' and implies its a finite number. The person asking almost always then goes on to push that there's two because that's "how its always been" and then folks can't get gender affirming care are are essentially classified as "nonexistent".
The right, being rooted in conservatism, loves to ressurect old arguments in the name of " just asking questions" and have the rest of us redo the battles of old. For example, race science is discredited pseudoscience, there's no need to keep bringing it up unless you're trying to use it for, imo nefarious, political means.