>What's surprising is how often I encounter fellow Americans mistakenly asserting the first amendment extends beyond government and into the private sector.

I've only ever heard people complaining that people misunderstand the first amendment. I've yet to see someone say they believe the first amendment governs and protects against private censorship.

However, I constantly see people conflating the concept of free speech and the first amendment. Free speech is an ideological principle, not a law.

If you read the first section of the EO it is clear that they are attempting to make an argument that Twitter, by moderating/curating/screening, is no longer protected by section 230, as defined by the famous 90s court cases regarding prodigy, aol, and compuserve. [0] [1]

Spurious argument or not you are mischaracterizing the situation.

[0] https://en.wikipedia.org/wiki/Stratton_Oakmont,_Inc._v._Prod....

[1] https://en.wikipedia.org/wiki/Zeran_v._America_Online,_Inc.