Let's have a constitutional review, shall we? It seems like we need it.
The First Amendment prevents the GOVERNMENT from making laws that prohibit free speech, AND protects the right to petition the government. /1 of 5

Twitter and Facebook are not the government. Speech on a commercial platform owned by someone else is not protected free speech. The government can't stop you from tweeting bullshit, but Twitter can. They own the platform and make the rules. /2

The Communications Decency Act leaves a cutout for platform operators that relieves them of the duty to moderate indecent content. That does not prohibit them from doing so, or from flagging content that is bullshit. The cutout was to protect them from liability for boob pics. /3

The Communications Decency Act is not part of the Constitution. It is irrelevant in this context.
The First Amendment, in fact, protects Twitter's right to call bullshit on things on their platform. It protects *their* speech from the government's censorship, /4

So, the Trump EO as written violates Twitter's 1st Amendment rights. It does not enforce anyone else's. If you want a platform to spew bullshit on without having to deal with terms of service, build your own. /5, fin

PS: I don't think I'm saying anything controversial in this thread. The controversy is that actually reading the documents cited by people shouting about Free Speech and parsing the facts of law is controversial.