Actually no. You are conflating "First Amendment" and "freedom of speech". The First Amendment only gives us the legal right of free speech in regards to our government. Free speech, on the other hand, is determined by some major dictionaries to be inherently related to a government, but many others (including Oxford), in no way attach the definition of free speech to a government. Free speech can be decided upon by any group that has power over the medium of speech. If the moderators and admins of voat decided that there would be unadulterated free speech there, they would have granted free speech to the users of their platform. That is what people who advocate for free speech on these sites are pushing for.

You also seem to be misunderstanding the entire point. No one is saying that reddit and voat don't have the legal right to censor people. Absolutely no one. Your entire argument is basically saying "It's their website, they can censor what they want." That is just arguing against a straw man. What people are arguing about is the moral implication of people who own these massive forums having such massive control over the flow of information and conversation.

I don't use voat, nor do I use any of the subreddits that have been quarantined/banned/whatever. However, on one of my alts I used to be a moderator of r/sandersforpresident. I can tell you that in their group chat, they would sometimes even openly discuss how to best get rid of posts that made Sanders supporters look bad. They intentionally left some of the rules vague enough to allow that kind of discretion. And yes, it was totally within their rights to do that. They are the ones who have power over the forum. But the argument isn't whether they can do that, but whether they should. I would posit that they shouldn't. I further guarantee that they are far from the only subreddit to engage in such tactics. When massive sites like reddit allow this to happen, it makes it harder to communicate your ideas. Impossible? No. But significantly more difficult? Yes. And again, I'm not arguing that they can't do this, just that they shouldn't, as they have immense power over the flow of information.