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.