A bar is private property that just so happens have the doors open for potential customers, whilst some things on the internet are public access, nobody is forcing you to go to any specific website if you don't want to, but at a privately owned bar you might not like someone chanting about politics or whatever the case may be, and this is established laws for platforms vs publishers in the USA. This is why a lot of people have issues with Google editorializing search results (check out Project Veritas on the matter) because they reach out into editor territory and out of just being a platform.
Since somebody downvoted without providing references to their refutes here's an actual case about freedom of speech online which is the main one by the looks of it in regards to suppressing speech online:
https://en.wikipedia.org/wiki/Reno_v._American_Civil_Liberti...
The burden of defamation is on the person not the website if anything, however, if someone posts anonymously who do you sue? The best a platform can do is delete their account. I've successfully had defamatory / false content about myself deleted from a platform in the past.