I recently deleted a post of a user because I considered it off-topic and driving a discussion into an unconstructive direction. When the user reposted the same post a few minutes later, I deleted it again and banned the user.
The user then created a new account and complained that they have a constitutional right to freedom of speech and I would violate it by deleting their posts and banning them. Do they have a point?
People generally are confused about the nature of a website. They see that it is something they can just freely enter from anywhere and assume it is public, but a store is a better comparison. You don't pay to enter a store and anyone can enter, but it is still private property. This is why Terms of Service on websites exist and why they have any value at all.
When someone goes to a website, they are consuming resources of that site and they are only allowed to do so because they are granted permission to be on the premise of the site. It is truly private property and in fact most hacking computer crimes are effectively trespassing as they are making unapproved use of private resources.
Similarly, if someone is participating within a privately run community (which any website is) they have no right to do anything other than to leave or do what the owner of the property says.
What freedom of speech does protect is someone's right to say what they want, on their own property or in public property (in most cases) without fear of retribution from the government. Note that there also isn't a right to be heard, just to be able to speak. If you were trying to support something and stood up on a street corner, there is nothing wrong with 100 people who oppose it gathering around you and drowning you out. They aren't impeding on your right to speak, they are just speaking louder.
The right to freedom of speech only means you can say what you want without penalty simply for saying it, even if it is unpopular. It doesn't mean private companies or individuals can't possibly treat you differently (as long as it isn't discriminatory) or that you can't be ignored completely. It just means you can say your peace without fear of government action. You can't require anyone else to help you broadcast it with their resources. You can't require people to hear it.
If they want to start their own site and make their post, they are welcome to do so, but you are under no obligation to allow them to say it on your system. It might become slightly more tricky if your site was operated by the government or a publicly owned entity, but even then, being outside the context of the site would probably be sufficient. (As long as it is actually outside the context.) The real world parallel there would be that you can't go marching in to Congress and talk about whatever you want, even though it is public, because it isn't what that public space is for.
Freedom of speech means that the government can't punish them for what they say. It doesn't mean that you can't do so in your community.
When you moderate a community, you have a house-right. You have the right to evict anyone from the community for any reason you see fit. The content users post is served by your system, and you are under no obligation to serve any and all data people submit to it. You have the right to delete any user-submitted content you don't like.
So when a user argues that their right to freedom of speech is violated, then point out that they still have the right to say wherever they want (as long as it doesn't violate other laws), just not in your community. They are free to exercise their right on any other websites which tolerates it. When they don't find such a website, they are free to build their own. But you are under no obligation to offer them a platform for their speech when you don't want to.
There is also a related XKCD comic.
However, keep in mind that an authoritarian moderation style can not just drive away the people you want to drive away. Many community participants enjoy an open discussion culture where diverse and even controversial viewpoints can be discussed without being afraid of getting hit by the banhammer. Also, posts disappearing without explanation can often create an Orwellian atmosphere of hidden censorship.
So while you are not obliged to allow total freedom of speech in your community, you should consider tolerating it to a certain degree in the interest of building a friendly and welcoming community. Also, when you delete content you should consider making it transparent with a short post explaining that you deleted content and why. This also helps to communicate to the community which speech is acceptable in your community and which isn't.
Simply put, the forum and the website are private properties. It's in your right to moderate, suspend or ban users from your platforms as you see fit.
As harsh as that sounds, you have to remember that you are likely managing a communication platform. Therefore, anything can be a form of freedom of speech. If you could do nothing about that, then why would you exist? Why would rules exist? It would be complete anarchy with human sacrifice, dogs and cats living together... mass hysteria!
Sometimes being open about that with users will make them understand.
I recently deleted a post of a user because I considered it off-topic and driving a discussion into an unconstructive direction.
When the user reposted the same post a few minutes later, I deleted it again and banned the user.
The user then created a new account and complained that they have a constitutional right to freedom of speech and I would violate it by deleting their posts and banning them. Do they have a point?
Probably not. They were banned and they're upset and annoyed, and in my experience they're going to complain about your site because they want to 'hurt' it. It doesn't necessarily mean that they feel like they don't have 'freedom of speech'.
