“it was open for use by the public”

The ruling makes clear a company town is not a private forum. One thing that separates that company town or shopping mall from say a private resort is the requirements for access. Cruse ships, aircraft, etc default deny entry making them less public spaces.

Beyond that, a private home can deny access based on skin color while a bed and breakfast can’t. That same bed and breakfast could however deny access because a customer is rude.

> The first one was decided on the basis of the US Constitution's First Amendment.

Yes, but much more narrowly than you're trying to apply it.

Subsequent decisions made clear internet services are not the same as company towns.

https://en.wikipedia.org/wiki/Marsh_v._Alabama

> The Marsh holding at first appears somewhat narrow and inapplicable today because of the disappearance of company towns from the United States, but it was raised in a somewhat high-profile 1996 cyberlaw case, Cyber Promotions v. America Online, 948 F. Supp. 436, 442 (E.D. Pa. 1996).[1] Cyber Promotions wished to send out "mass email advertisements" to AOL customers. AOL installed software to block those emails. Cyber Promotions sued on free speech grounds and cited the Marsh case as authority for the proposition that even though AOL's servers were private property, AOL had opened them to the public to a such a degree that constitutional free speech protections could be applied. The federal district court disagreed, thereby paving the way for spam filters at the Internet service provider level.

True but to apply 1A it had to be determined that the constitutional protections were applicable at all which hinged on the level the area had been "dedicated/opened to public use" more recently other qualifiers have been added such that a company needs to exercise "powers traditionally exclusive to the state" to be held to constitutional standards. There were cases back years ago like Cyber Promotions v. America Online that allowed companies to limit speech on their platforms that would already cover cases like this too.

> Also, I was responding to a blanket assertion that you have no constitutional rights in a private forum. A company town is a private forum.

But your own stuff explicitly stated that the courts did not deem it a private forum but was a public form.

Websites are not the same thing, so yes a website is still a private forum and therefore not in violation of 1A.