"The first amendment" is a synecdoche for free speech rights in the US in general. Those don't disappear when you step into a private space, rather the free speech rights are just balanced against property rights.

don’t perpetuate the myth that the first amendment applies to any non-government entity.

OK but. https://www.law.cornell.edu/constitution-conan/amendment-1/quasi-public-places

In Marsh v. Alabama,2 the Court held that the private owner of a company town could not forbid distribution of religious materials by a Jehovah’s Witness on a street in the town’s business district. The town, wholly owned by a private corporation, had all the attributes of any American municipality, aside from its ownership, and was functionally like any other town. In those circumstances, the Court reasoned, “the more an owner, for his advantage, opens up his property for use by the public in general, the more do his rights become circumscribed by the statutory and constitutional rights of those who use it.”

I would argue that the stadium, probably built with public funds, functions as a public space, and with the amount of public support for sports teams generally, I'd say theyre quasi-public too.

US courts would disagree with me at the moment (as the latter unquoted part of my link shows), but it's not as farfetched a legal theory as you imply. And like I said before, "first amendment" is used as a phrase to talk about free speech generally, even if it's not strictly making a constitutional legal argument. Its an ideal to be upheld

Tl;Dr: you're 100% correct in the current political climate. But scotus cases can be overturned. https://en.wikipedia.org/wiki/Lloyd_Corp._v._Tanner is a more relevant case than marsh v Alabama, and it's not set in stone (good luck getting the dictatorship of the bourgeoisie to overturn it, but it's not crazy)