This is where the true disagreement is. We can both believe in the constitution, in the first amendment, and in section 230, but I don't believe social media is a public space, because the person paying for the server is not the government. To me, these are very explicitly private organizations running web applications. For it to be a public space, it would necessarily not be limited in existence to the ability of a private organization to keep it running profitably.
Madison Square Garden is a private space, because someone owns it; it cost money to build, it costs money to maintain, there are finite seats, etc. The organization paying for the thing to exist has authority over the thing. If you want a public space, you can either create one explicitly, or petition the government to create a social media platform bound by the first amendment. It isn't Reddit or Twitter. Those are someone else's property.