The argument GP is making is that if the government can't make it illegal, private companies shouldn't disallow it; the person you're replying to is pointing out that the First Amendment sets that bar far higher than GP probably realized.
This is not historically the reality of 1a jurisprudence. Before the Internet, the ruling was that private companies cannot restrict your speech in public view. See Marsh v. Alabama for this -- a company town was prohibited from barring picketing and pamphleting on private sidewalks.
The exceptions to this were carved out in a court case regarding Compuserve, which was a subscription-only service. The stare decisis in this instance is on far shakier ground than Roe was.
You have to register to use twitter. Marsh v Alabama had nothing to do with compuserve. That would matter if a website was truly a de facto public square, but given the whole registration thing, they're not.
The compuserve case led to section 230 of the CDA being created, but again that doesn't have to do with Marsh v Alabama. To have that apply, you'd need to make the argument that Twitter both is, and intends to be a public square, and well, the fact that they have posted moderation policies makes it clear that they don't.
Marsh was not the public square. It was the sidewalks of random streets. The company that owned them explicitly did not intend for them to be a public square.
In contrast, the historical statements of Twitter make it very clear that they intended to be the public square, e.g. "free speech wing of the free speech party." Additionally, the assertions and decisions of the state in regards to social media indicate massive influence over politics that far exceeds any city street. They say people are denied their rights of free expression because Trump blocked them on Twitter, and that Russia successfully manipulated our elections because a few Russians bought a tiny amount of Facebook ads.
> It was the sidewalks of random streets. The company that owned them explicitly did not intend for them to be a public square.
Sidewalks of random streets are considered to be "the public square" in US law (broadly because random streets are usually publicly owned. You need things like gates and signs and such to revoke such an assumption). The Marsh v. Alabama ruling relied on the fact that the town didn't try to make its streets un-square like, and in fact encouraged public square-like use!
> In contrast, the historical statements of Twitter make it very clear that they intended to be the public square, e.g. "free speech wing of the free speech party."
You will be hard pressed to take a single statement, made by a minor executive who acts outside of US jurisdiction, in 2012, as superior to the actual user agreements that Twitter has (and had at the time) in the US.
