> But if we don't oppose pro-murder propaganda, those people will still look for ways to censor ideas I support.
I can expand on this if you're really curious. The short version is that I don't think it's realistic to expect reciprocal generosity from a party that clearly has a double standard about what is and isn't censorship. But on the other hand, we can make a choice not to literally hand that party ammunition for their arguments.
We know that laws around censorship are disproportionately targeted at minority/oppressed communities. We have over 100 years of history demonstrating that fact, from the draft protests, to McCarthyism, to the mass-deplatforming and threatening of the LGBTQ+ community, to moral panics about satan worshiping and sex in mainstream media. We also know the arguments that those people use to try and further their agendas.
They will still use those arguments even if we have Free Speech principles. The difference is that neutral observers will be able to tell that they're being hypocritical. The difference is that they'll have fewer laws on the books that they can quickly repurpose to their agenda.
When you know what someone's strategy is to attack you, when you know how Republicans are going to try and disrupt protests and attack critics, you don't play into that strategy. You try to set up an environment that is hostile to their talking points. That's how Free Speech advocacy responds to bigots -- it tries to make a general social environment where, for example, the recent Florida laws trying to shut down protests look unusual and bad and repressive even to casual observers who haven't researched the issues.
We don't expect racists and homophobes to play fair, that's why we're building a set of laws and social standards that make it harder for them to argue that it's OK to pull funding from schools that teach critical race theory. These people are better at censoring than you are; if you let them set all of the rules of engagement, then they will win.
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The opposite is also true. Free Speech and Free Association are more helpful to progressive organizations than they are to regressive movements, because most of the time regressive movements are trying to shut down conversation and to stop social evolution. You can see this happening with critical race theory, you can see this happening with BLM protests, you can see it pop up with recent efforts to restrict counseling and support structures for LGBTQ+ youth. You can even see it with how much Conservatives have freaked out over company statements on voting rights and business decisions not to work with states that pass regressive laws. Regressive movements talk a big game about Free Speech, but so much of their ideology depends on nobody questioning the status quo of how we think about race, gender, and inequality, and on punishing and ostracizing anyone in their communities that listens to critics or evolves their views over time.
Sure, they'll use Free Speech to try and argue against Freedom of Association or to claim that they're being oppressed because a football player had the "audacity" to talk about race in a public setting, but they're not particularly good at that kind of rhetoric. The arguments are ultimately unpersuasive and it's relatively easy to point out how they're being hypocritical. So by creating an environment that is Free Speech friendly, not only do we make their ideas about oppression less persuasive and harder to implement -- we also play to our strengths. We create an environment where it is easier to educate people about issues like trans liberation and to showcase the radical inequalities that exist in America. I don't think it's an accident that LGBTQ+ rights have progressed faster than other historical pushes for equality in an environment where it's easier than ever before to share information about people's day-to-day struggles and experiences. So much of regressive ideology relies on people being able to block out progressive movements and to filter/mischaracterize what progressive movements say.
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So long story short, TLDR regressive/bigoted movements do abuse Free Speech to defend themselves, but it's mostly rhetoric. They are more reliant on censorship than on a free flow of information to further their goals. To the extent that they really care about Free Speech, they're mostly just arguing to get rid of Freedom of Association and to force people to stop criticizing them or kicking them out of privately owned spaces.
So when we build societies that are resistant to censorship, we're not saying that those people will play along and respect our rules. And we do accept that on the tail-end of certain movements (esp conspiracy theories), Free Speech does genuinely make our job harder. But what we're trying to do is to create a battlefield for progressivism that (overall) plays to our strengths and exploits their weaknesses.